Algebra and Trigonometry: Real Mathematics, Real People (7th Edition)

Chapter 10

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3579 ; To compute the first term of the sequence, ... more

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; To compute the first term of the sequence, ... more

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6,7,8,9,10 ; Obtain the second term of the ... more

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134711 ; To compute the second term of the ... more

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245 ; To compute the zeroth term of the sequence, ... more

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; Expand  the factorials. ; To simplify the ... more

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44 ; Expand the sum while substituting to .  ; ... more

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is equivalent to , and in expression , 3 is ... more

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     ; ; ; ; Since a cube placed in the center is ... more

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Terms ; An infinite sequence is a function with ... more

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Recursively ; In a sequence, if one or  more terms... more

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IndexUpper limitLower limit ; The notation of the ... more

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Series ;   Here, is called the index of summation... more

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  ; If is a positive integer, then is, Therefore... more

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135 ; To compute the first term of the sequence, ... more

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15913 ; To compute the first term of the sequence... more

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392781243 ; To compute the first term of the ... more

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  ; To compute the first term of the sequence, ... more

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; To compute the first term of the sequence, ... more

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416 ; To compute the first term of the sequence, ... more

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2 ; To compute the first term of the sequence, ... more

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; To compute the first term of the sequence, ... more

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; To compute the first term of the sequence, ... more

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1 ; To compute the first term of the sequence, ... more

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9, 15, 21, 27, 33, 39, 45, 51, 57, 63 ; Enter the ... more

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, 5, 17, 33, 53, 77, 105, 137, 173, 213 ; Enter ... more

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3, 2.5, 2.33, 2.25, 2.2, 2.17, 2.14, 2.125, 2.11, ... more

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1.333, 4, 7.2, 10.667, 14.286, 18, 21.778, 25.6, ... more

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0, 2, 0, 2, 0, 2, 0, 2, 0, 2 ; Enter the sequence ... more

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9, 7, 9, 7, 9, 7, 9, 7, 9, 7 ; Enter the sequence ... more

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; To compute the 10th term of the sequence, ... more

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; To compute the 10th term of the sequence, ... more

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; To compute the 25th term of the sequence, ... more

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; To compute 16th term of the sequence, ... more

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; To compute 7th term of the sequence, substitute... more

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; To compute the 6th term of the sequence, ... more

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; Compare the terms of the sequence with the ... more

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; Compare the terms of the sequence with the ... more

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; Compare the terms of the sequence with the ... more

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; Compare the terms of the sequence with the ... more

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; Compare the terms of the sequence with the ... more

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; Compare the terms of the sequence with the ... more

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; Compare the terms of the sequence with the ... more

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; Compare the terms of the sequence with the ... more

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; Compare the terms of the sequence with the ... more

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; Compare the terms of the sequence with the ... more

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; Compare the terms of the sequence with the ... more

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; Compare the terms of the sequence with the ... more

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; Compare the terms of the sequence with the ... more

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; Compare the terms of the sequence with the ... more

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2824201612 ; To compute the second term of the ... more

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1518212427 ; To compute the second term of the ... more

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3461018 ; To compute the second term of the ... more

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3216842 ; To compute the second term of the ... more

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134711 ; To compute the second term of the ... more

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54913 ; To compute the second term of the sequence... more

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: 6; : 8; : 10; : 12; : 14: ; To find the second ... more

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: 25; : 20; : 15; : 10; : 5: ; To find the second ... more

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: 81; : 27; : 9; : 3; : 1: ; To find the second ... more

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: 14; : ; : 56; : ; : 224: ; To find the second ... more

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; Operate the factorial. ;   ; Simplify the ... more

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; Operate the factorial. ;   ; Simplify the ... more

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495 ; Operate the factorial. ;   ; To simplify the... more

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5040 ; Operate the factorial. ;   ; To simplify ... more

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; Operate the factorial. ;   ; To simplify the ... more

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; Operate the factorial. ;   ; To simplify the ... more

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; Operate the factorial. ;   ; To simplify the ... more

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; Operate the factorial. ; To simplify the ... more

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As the value of tends to infinity, the value of ... more

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Enter the sequence into the CAS. ; The graph ... more

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Enter the expression into the sequence mode of CAS... more

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Enter the expression into the sequence mode of CAS... more

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Enter the expression into the sequence mode of CAS... more

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Enter the sequence into the CAS. ; The graph ... more

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Enter the sequence into the CAS. ; The graph ... more

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35 ; Expand the sequence from lower limit to upper... more

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57 ; Expand the sequence from lower limit to upper... more

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364 ; Expand the sequence from lower limit to ... more

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165 ; Expand the summation from to .  ; Perform ... more

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; Expand the summation from to .  ; Perform the ... more

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; Expand the summation from to .  ; Perform the ... more

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; Expand the sum from to . ; Simplify the ... more

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20 ; Expand the sum from to .  ;   ; Simplify the... more

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186 ; Expand the sum from to . ; Perform the ... more

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64 ; Expand the sum from to . ; Perform the ... more

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31 ; Expand the sum from to . ; Perform the ... more

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11 ; Expand the sum from to .  ; Perform the ... more

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81 ; Enter the series into the CAS to obtain the ... more

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5.03 ; Enter the series into the CAS to obtain the... more

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0.63333 ; Enter the series into the CAS to obtain ... more

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0.375 ; Enter the series into the CAS to obtain ... more

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0.943  ; To write the sigma notation, use 9 as the... more

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11.9036 ; To write the sigma notation, use 15 as ... more

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33 ; To write the sigma notation, use 8 as the ... more

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3.4722 ; To write the sigma notation, use 6 as the... more

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546 ; To write the sigma notation, use 6 as the ... more

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0.66406 ; To write the sigma notation, use 6 as ... more

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0.82128 ; To write the sigma notation, use 20 as ... more

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0.246212 ; To write the sigma notation, use 10 as ... more

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2.0156 ; To write the sigma notation, use 5 as the... more

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18.25 ; To write the sigma notation, use 6 as the ... more

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; To compute the fourth partial sum, expand the ... more

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; To compute the fifth partial sum, expand the ... more

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; To compute the third partial sum, expand the ... more

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; To compute the fourth partial sum, expand the ... more

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True ; Apply the property of sum, in the left ... more

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True ; Compute the sum of the left side of the ... more

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1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 1, 2... more

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Entire Proof Answer: Replace by in and then ... more

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; Enter the sequence into the CAS to obtain the ... more

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Fibonacci sequence ; To compute the first four ... more

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; To compute the th term of the sequence, replace... more

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Yes because the given identity is the recursive ... more

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; To compute the first term of the sequence, ... more

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; To compute the first term of the sequence, ... more

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     ; To compute the first term of the sequence, ... more

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     ; To compute the first term of the sequence, ... more

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     ; To compute the first term of the sequence, ... more

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     ; To compute the first term of the sequence, ... more

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     ; To compute the first term of the sequence, ... more

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; To compute the first term of the sequence, ... more

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     ; To compute the first term of the sequence, ... more

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     ; To compute the first term of the sequence, ... more

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; To calculate the first term of the sequence, ... more

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; To calculate the first term of the sequence, ... more

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; To calculate the first term of the sequence, ... more

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; To calculate the first term of the sequence, ... more

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Yes, a finite series of integers have a finite sum... more

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2, 5, 8, 11 ; Substitute in to compute the first... more

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; Substitute and in the formula for the term... more

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, 1, 5, 9, 13, 17, 21, 25, 29, 33, 37  ; Relate ... more

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; Compute the common difference by calculating ... more

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217 ; Notice that the common difference in the ... more

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43560 ; Compute the common difference by ... more

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; The annual sales are in arithmetic sequence in ... more

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All the sequences are arithmetic sequences. ; ... more

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; is used to calculate the term of an arithmetic... more

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The sum of a finite arithmetic sequence with ... more

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A sequence is an arithmetic sequence if the ... more

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The common difference of an arithmetic sequence ... more

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Arithmetic sequence ; Compute the difference ... more

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Arithmetic sequence  ; Compute the difference ... more

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Arithmetic sequence  ; Compute the difference ... more

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Arithmetic sequence  ; Compute the difference ... more

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Not an arithmetic sequence. ; Compute the ... more

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Not an arithmetic sequence. ; Compute the ... more

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21, 34, 47, 60, 73Arithmetic sequence ; Substitute... more

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143, 136, 129, 122, 115Arithmetic sequence ; ... more

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25, 21, 17, 13, 9Arithmetic sequence ; Substitute... more

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1, 5, 9, 13, 17Arithmetic sequence ; Substitute ... more

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3, 6, 11, 20, 37Not an arithmetic sequence.  ; ... more

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1, 2, 4, 8, 16Not an arithmetic sequence.  ; ... more

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1, 5, 1, 5, 1Not an arithmetic sequence. ; ... more

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, 1, , 1, Not an arithmetic sequence.  ; ... more

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, , , , Arithmetic sequence ; Substitute in the ... more

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, , , ,  Arithmetic sequence  ; Substitute in the... more

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; Substitute and in the formula for term . ; ... more

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; Substitute and in the formula for term . ; ... more

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; Substitute and in the formula for term . ; ... more

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; Substitute and in the formula for term . ; ... more

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; Compute the common difference by calculating ... more

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; Compute the common difference by calculating ... more

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; Relate of the arithmetic sequence with . ; ... more

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; Relate of the arithmetic sequence with . ; ... more

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; Relate of the arithmetic sequence with . ; ... more

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; Relate of the arithmetic sequence with . ; ... more

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5, 11, 17, 23, 29 ; Substitute, and in the term... more

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5, , , , 2 ; Substitute, and in the term ... more

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, , , , ; Substitute, and in the term formula... more

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, , 8, 17, 26 ; Substitute, and in the term ... more

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, 2, 6, 10, 14 ; Relate of the arithmetic ... more

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, , , , ; Relate of the arithmetic sequence with... more

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22.45, 20.725, 19, 17.275, 15.55 ; Relate of the ... more

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: 6; : ; : 11; : ; : 16 ; Since and are 9 terms ... more

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15, 19, 23, 27, 31   ; Substitute, in . ; ... more

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6, 11, 16, 21, 26 ; Substitute, in . ; Substitute... more

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, , , , ; Substitute, in . ; Substitute, in to ... more

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1.5, , , , ; Substitute, in . ; Substitute, in ... more

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59 ; Relate of the arithmetic sequence with .... more

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83 ; Relate of the arithmetic sequence with .... more

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; Relate of the arithmetic sequence with .... more

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; Relate of the arithmetic sequence with .... more

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Enter the expression into the sequence mode of CAS... more

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Enter the expression into the sequence mode of CAS... more

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Enter the expression into the sequence mode of CAS... more

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Enter the expression into the sequence mode of CAS... more

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, 3, 7, 11, 15, 19, 23, 27, 31, 35 ; Enter the ... more

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20, 23, 26, 29, 32, 35, 38, 41, 44, 47 ; Enter the... more

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19.25, 18.5, 17.75, 17, 16.25, 15.5, 14.75, 14, 13... more

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, , , 0.2, 1, 1.8, 2.6, 3.4, 4.2, 5 ; Enter the ... more

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1.55, 1.6, 1.65, 1.7, 1.75, 1.8, 1.85, 1.9, 1.95, ... more

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, , , , , , , , , ; Enter the sequence into the ... more

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110 ; Notice that the common difference in the ... more

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70 ; Notice that the common difference in the ... more

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; Notice that the common difference in the ... more

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; Notice that the common difference in the ... more

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5050 ; The first 100 positive integers are 1, 2, 3... more

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; The first 50 negative integers are , , ,..., ... more

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; Notice that the common difference of the ... more

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1220 ; Notice that the common difference in the ... more

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620 ; Compute the common difference by calculating... more

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1850 ; Compute the common difference by ... more

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36 ; Compute the common difference by calculating ... more

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17.4 ; Compute the common difference by ... more

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4000 ; Substitute , and in the formula . ; Solve... more

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16,100 ; Substitute , and in the formula . ; ... more

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1275 ; Expand the series. ; Notice that the common... more

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10,100 ; Expand the series. ; Notice that the ... more

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355 ; Expand the series. ; Notice that the common ... more

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2500 ; Expand the series. ; Notice that the common... more

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129,250 ; Expand the series. ; Notice that the ... more

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218,625 ; Expand the series. ; Notice that the ... more

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440 ; Enter the series into the CAS to obtain the ... more

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; Enter the series into the CAS to obtain the sum... more

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; Enter the series into the CAS to obtain the sum... more

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; Enter the series into the CAS to obtain the sum... more

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14,268 ; Enter the series into the CAS to obtain ... more

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2602.5 ; Enter the series into the CAS to obtain ... more

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405 bricks ; Number of bricks in the patio are in ... more

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590 ; Number of seats in the auditorium are in ... more

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; Annual profits are in arithmetic sequence in ... more

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; Compute the common difference by calculating ... more

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True. Use the formula .  ; Relate the term of the... more

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False ; If the first term and term is known, the ... more

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, , , , , , , , ,   ; Substitute and in the ... more

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, , , , , , , , , ; Substitute and in the term ... more

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Compute and use to find the term.  ; Consider ... more

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4 ; Substitute in the sum formula . Here, ... more

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; is used to calculate the term of an arithmetic... more

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; Person C calculates the sum of numbers from 1 ... more

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Statement (b) is false. ; Refer to the given ... more

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; The given system of linear equation is aligned... more

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; The given system of linear equation is aligned... more

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The net sales of the dollar tree were million, ... more

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2496 ; Substitute the values in the expression ... more

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2; 8; 32; 128; 512 ; The first term is 2.... more

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; Substitute 12 for , 14 for , and for into the... more

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195312500 ; Calculate the common ratio by ... more

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; The relation between fifth term and the second ... more

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; Express the summation by writing a few terms of... more

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; Use the Compound Interest formula  to find the ... more

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The first term is entered incorrectly. ; In the ... more

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The sum of infinite terms is infinite when the ... more

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GeometricCommon ratio ; A sequence in which the ... more

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; The formula for the th term of the geometric ... more

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Geometric series ; Infinite geometric sequence ... more

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No  ; A sequence is a geometric sequence if the ... more

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; Infinite geometric sequence contains an ... more

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Geometric sequence ; To compare the ratio of ... more

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Geometric sequence ; To compare the ratio of ... more

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Not a geometric sequence  ; To compare the ratio ... more

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Not a geometric sequence  ; To compare the ratio ... more

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Geometric sequence ; To compare the ratio of ... more

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Geometric sequence ; To compare the ratio of ... more

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Geometric sequence ; To compare the ratio of ... more

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Geometric sequence ; To compare the ratio of ... more

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Not a geometric sequence  ; To compare the ratio ... more

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Not a geometric sequence ; To compare the ratio of... more

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6; 18; 54; 162; 486 ; The first term is 6. ... more

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4; 8; 16; 32; 64 ; The first term is 4.Substitute ... more

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1; ; ; ; ; The first term is 1.Substitute 2 for , ... more

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2; ; ; ; ; The first term is 2.Substitute 2 for , ... more

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5; ; ; ; ; The first term is 5.Substitute 2 for , ... more

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6; ; ; ; ; The first term is 6.Substitute 2 for , ... more

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9; ; ; ; ; The first term is 9.Substitute 2 for , ... more

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7; ; 35; ; 175 ; Substitute 2 for , 7 for , and ... more

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64321684 ; To calculate the second term of the ... more

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8127931 ; To calculate the second term of the ... more

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9183672144 ; To calculate the second term of the ... more

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51545135405 ; To calculate the second term of the ... more

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6-9 ; To calculate the second term of the sequence... more

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30-20 ; To calculate the second term of the ... more

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; To calculate the common ratio , divide the ... more

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  ; To compute the common ratio , divide the ... more

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; To compute the common ratio , divide the second... more

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  ; To compute the common ratio , divide the ... more

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; Write the relation between the first and the ... more

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; Write the relation between the first and the ... more

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; Write the relation between the second and the ... more

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; Write the relation between the second and the ... more

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Enter the expression into the CAS. ;     ; The ... more

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Enter the expression into the sequence mode of CAS... more

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Enter the expression into the sequence mode of CAS... more

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Enter the expression into the sequence mode of CAS... more

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; To calculate the first partial sum, substitute ... more

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; To calculate the first partial sum, substitute ... more

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16,24,28,30,31,31.5,31.75,31.875,31.9375,31.96875... more

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4,4.8, 4.96, 4.992, 4.9984, 4.99968, 4.999936, 4.... more

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511 ; Expand the summation of the sequence. ; To ... more

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171 ; Expand the summation of the sequence. ; To ... more

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43 ; Expand the summation of the sequence. ; To ... more

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42.65625 ; Expand the summation of the sequence... more

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2700.3072 ; Expand the summation of the sequence... more

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646.80544 ; Expand the summation of the sequence... more

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6.4 ; Expand the summation of the sequence. ; To ... more

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3.749936 ; Expand the summation of the sequence... more

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2092.60 ; Expand the summation of the sequence. ; ... more

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3949.14724 ; Expand the summation of the sequence... more

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; Rewrite the sequence, as,,to compute the   ... more

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; Rewrite the sequence, as,,to compute the   ... more

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; Rewrite the sequence, as,, to compute the   ... more

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; Rewrite the sequence, as,, to compute the   ... more

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50 ; Express the summation of the sequence by ... more

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18 ; Express the summation of the sequence by ... more

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; Expand the summation of the sequence by writing... more

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4 ; Express the summation of the sequence by ... more

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Does not have a finite sum ; Express the summation... more

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Does not have a finite sum ; Express the summation... more

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11.236 ; Express the summation of the sequence by ... more

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9.091 ; Express the summation of the sequence by ... more

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; Express the summation of the sequence by ... more

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; Expand the summation of the sequence by writing... more

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27 ; Rewrite the summation of the sequence by ... more

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32 ; Rewrite the summation of the sequence by ... more

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Does not have a finite sum ; Rewrite the summation... more

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Does not have a finite sum. ; Rewrite the ... more

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; Rewrite the summation of the sequence by ... more

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-3.2727 ; Rewrite the summation of the sequence by... more

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; Suppose ; multiply both sides of by 100 as ... more

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; Suppose ; multiply both sides of by 1000 as ... more

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; Suppose ; multiply both sides of by 10 as ... more

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; Suppose ; multiply both sides of by 10 as ... more

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Geometric sequence 262136 ; Consider the sequence ... more

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Arithmetic sequence ; Consider the sequence ... more

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Geometric sequence135 ; Consider the sequence ... more

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Arithmetic sequence ; To compare the difference ... more

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Arithmetic sequence720 ; Expand the summation of ... more

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Geometric sequence7174453 ; Expand the summation ... more

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Geometric sequence28.94448 ; Expand the summation ... more

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Arithmetic sequence ; Expand the summation of the ... more

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; Rewrite the sequence associated with the series... more

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; Rewrite the sequence associated with the series... more

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Use the formula for the sum of finite geometric ... more

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Use the formula for the sum of finite geometric ... more

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126 square inches ; The length of each side of the... more

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; Calculate the area of the first square by ... more

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42 feet ; Initially, the ball is dropped from a ... more

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False ; Write the provided information ... more

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True ; Write a geometric sequence with the first ... more

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False ; Suppose a geometric sequence with the ... more

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3,,,, ; Compute the second term of the sequence by... more

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; Compute the second term of the sequence by ... more

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; To compute the 9th term of the sequence, ... more

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; To compute the 6th term of the sequence, ... more

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The term of a geometric sequence is given by . ... more

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The term of any geometric sequence can be ... more

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; Let the given matrix be .The value of if . ... more

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; Let the given matrix be .The value of if . ... more

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; Find the binomial coefficients using , where ... more

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; Find the binomial coefficients using , where ... more

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; Find the binomial coefficients using , where ... more

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: 1; : 9; : 36; : 84; : 126; : 126;: 84; : 36; : 9... more

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The values of and are always equal. ... more

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                ; Binomial expansion is performed ... more

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ExpandingBinomial ; To simplify or find any term ... more

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Binomial theoremPascal triangle ; Pascal triangle ... more

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3 ; Since the formula for the binomial theorem is... more

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21 ; Write the combination in factorial form. ; ... more

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28 ;  Write the combination in factorial form. ; ... more

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15,504 ;  Write the combination in factorial form... more

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50,388 ; Write the combination in factorial form... more

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14 ; Write the combination in factorial form.  ; ... more

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153 ; Write the combination in factorial form. ; ... more

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1 ;  Write the combination in factorial form. ; ... more

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1 ;  Write the combination in factorial form. ;  ... more

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210 ; Write the combination in factorial form. ; ... more

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210 ; Write the combination in factorial form. ; ... more

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4,950 ; Write the combination in factorial form... more

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4,950 ; Write the combination in factorial form... more

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749,398 ; Enter the expressions into the CAS to ... more

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46,376 ;  Enter the expressions into the CAS to ... more

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230,300 ; Enter the expressions into the CAS to ... more

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124,750 ; Enter the expressions into the CAS to ... more

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 31,125 ;  Enter the expressions into the CAS to ... more

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499,500 ; Enter the expressions into the CAS to ... more

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; Find the binomial coefficients using , where ... more

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; Find the binomial coefficients using , where ... more

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; Find the binomial coefficients using , where ... more

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;  Find the binomial coefficients using , where ... more

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; Find the binomial coefficients using , where ... more

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; Find the binomial coefficients using , where ... more

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; Find the binomial coefficients using , where ... more

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;  Find the binomial coefficients using , where ... more

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; Find the binomial coefficients using , where ... more

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;  Find the binomial coefficients using , where ... more

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;  Find the binomial coefficients using , where ... more

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;  Find the binomial coefficients using , where ... more

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; Find the binomial coefficients using , where ... more

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; Find the binomial coefficients using ,where ... more

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; Find the binomial coefficients using , where ... more

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;  Find the binomial coefficients using , where ... more

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; Find the binomial coefficients using , where ... more

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; Find the binomial coefficients using , where ... more

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; Find the binomial coefficients using , where ... more

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;  Find the binomial coefficients using ,where ... more

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; Find the binomial coefficients using ,where ... more

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; Find the binomial coefficients using , where ... more

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; Find the binomial coefficients using , where ... more

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; Find the binomial coefficients using , where ... more

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;  Find the binomial coefficients using , where ... more

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; Find the binomial coefficients using , where ... more

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; Take the common term out and simplify the ... more

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; Take the common term out and simplify the ... more

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; Take the common term out and simplify the ... more

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; Take the common term out and simplify the ... more

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; Find the binomial coefficients using , where ... more

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  ; Find the binomial coefficients using , where ... more

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; Since the formula for the general term in the ... more

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; Since the formula for the general term in the ... more

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; Since the formula for the general term in the ... more

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; Since the formula for the general term in the ... more

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; Since the formula for the general term in the ... more

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; Since the formula for the general term in the ... more

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; Since the formula for the general term in the ... more

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; Since the formula for the general term in the ... more

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1,732,104 ; Write the term in the expansion of ... more

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32,440,320 ; Write the term in the expansion of ... more

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180 ; Write the term in the expansion of the ... more

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720 ; Write the term in the expansion of the ... more

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; Write the term in the expansion of the ... more

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90,720 ; Write the term in the expansion of the ... more

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210 ; Write the term in the expansion of the ... more

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792 ; Write the term in the expansion of the ... more

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35 ; Write the Pascal’s triangle. In Pascal's ... more

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20 ; Write the Pascal’s triangle. In Pascal's ... more

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6 ; Write the Pascal’s triangle. In Pascal's ... more

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10 ; Write the Pascal’s triangle. In Pascal's ... more

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; Write the binomial expansion up to the seventh ... more

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; Write the binomial expansion up to the seventh ... more

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; Write the binomial expansion up to the seventh ... more

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; Write the binomial expansion up to the seventh ... more

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; Write the binomial expansion up to the seventh ... more

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; Write the binomial expansion up to the seventh ... more

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; Find the binomial coefficients using where ... more

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; Find the binomial coefficients using where ... more

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; Find the binomial coefficients using , where ... more

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; Calculate the binomial coefficients using , ... more

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  ; Substitute the value of the function in the ... more

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  ; Substitute the value of the function in the ... more

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  ;  Substitute the value of the function in the ... more

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  ; Substitute the value of the function in the ... more

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; Find the binomial coefficients using , where ... more

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; Find the binomial coefficients using , where ... more

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; Find the binomial coefficients using , where ... more

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; Find the binomial coefficients using , where ... more

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; Find the binomial coefficients using , where ... more

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; Find the binomial coefficients using , where ... more

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; Find the binomial coefficients using , where ... more

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; Find the binomial coefficients using , where ... more

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; Find the binomial coefficients using , where ... more

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; Find the binomial coefficients using , where ... more

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1 ; Find the binomial coefficients using , where ... more

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; Find the binomial coefficients using , where ... more

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; Find the binomial coefficients using , where ... more

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; Find the binomial coefficients using , where ... more

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Approximately ; Expand the given expression. ; Use... more

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Approximately  ; Expand the given expression. ; ... more

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Approximately ; Expand the given expression. ; Use... more

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  ; Expand the given expression.  ;   ; Use the ... more

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The function shifts 2 units to the right of the ... more

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The function shifts 4 units to the left of the ... more

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The function shifts 5 units to the left of the ... more

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The function shifts 3 units to the right of the ... more

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; Expand the expression. ; Simplify the ... more

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  ; Expand the expression.  ;   ; Simplify the ... more

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  ; Expand the expression. ;   ; Simplify the ... more

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   ; Expand the expression.  ;   ; Simplify the ... more

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TrueThe numbers in Pascal’s triangle can be found ... more

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 FalseA binomial that represents the difference ... more

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; In the Pascal triangle, the number starts with ... more

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Compute the value of the expression on the left-... more

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Expand the binomial expression of and substitute ... more

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Use the formula to simplify the right side, . ... more

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Expand the binomial expression of and substitute ... more

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There will be negative sign with .The exponent of... more

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3 ; Count the number of ways that a sum of 14 can ... more

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A sum of 12 can be obtained in 36 different ways... more

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27,000  ; Apply the fundamental counting principle... more

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2,600,000  ; Apply the Fundamental Counting ... more

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24  ; Calculate the number of choices for the 4 ... more

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20   ; Calculate the number of choices for the ... more

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 1260  ; The word MITOSIS has 7 letters, out of ... more

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21 ; Use the formula for the number of ... more

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Fundamental Counting Principle. ; The Fundamental ... more

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Distinguishable permutations. ; If a set of ... more

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Permutation ; An ordering of elements such that ... more

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Total number of elements.The number of times the ... more

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8 ; The odd integers from 1 to 15 are 1, 3, 5, 7, ... more

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7 ; The even integers from 1 to 15 are 2, 4, 6, 8... more

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6 ; The prime integers from 1 to 15 are 2, 3, 5, 7... more

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4 ; From 1 to 15 there are 4 integers that are ... more

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11  ; Count the number of ways in which a sum of ... more

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9 ; Count the number of ways in which a sum of 22 ... more

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3 ; Count the number of ways in which a sum of 8 ... more

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3 ; Count the number of ways in which a sum of 24 ... more

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200 ; Apply the Fundamental Counting Principle to ... more

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30 ; Apply the Fundamental Counting Principle to ... more

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1024 ; Apply the Fundamental Counting Principle to... more

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 252 ; Apply the Fundamental Counting Principle to... more

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24,000,000 ; Apply the Fundamental Counting ... more

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175,760,000 ; Apply the Fundamental Counting ... more

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120 ; Calculate the number of choices for the ... more

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40,320 ; Calculate the number of choices for the ... more

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362,880 ; Calculate the number of choices for the ... more

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24 ; Calculate the number of possible orders of ... more

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24 ; Use the formula for the number of ... more

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120 ; Use the formula for the number of ... more

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336 ; Use the formula for the number of ... more

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380 ; Use the formula for the number of ... more

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720 ; Use the formula for the number of ... more

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840 ; Use the formula for the number of ... more

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427,518,000 ; Enter the given expression in the ... more

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1,814,400 ; Enter the given expression in the CAS ... more

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197,149,680 ; Enter the given expression in the ... more

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9,034,502,400 ; Enter the given expression in the ... more

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11,880 ; Calculate the number of choices of ... more

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1,816,214,400 ; Calculate the number of choices of... more

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1,092,624 ; Calculate the number of choices for ... more

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336 ; Use the formula to calculate the number of ... more

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ABCD, ABDC, ACBD, ACDB, ADBC, ADCB, BACD, BADC, ... more

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ABCD, ACBD, DBCA, DCBA  ; Total number of ... more

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420 ; The group of letters A, A, G, E, E, E, M has... more

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56 ; The group of letters B, B, B, T, T, T, T, T ... more

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2520 ; The group of letters A, L, G, E, B, R, A ... more

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34,650 ; The group of letters M, I, S, S, I, S, S... more

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10 ; Use the formula for the number of ... more

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20 ; Use the formula for the number of ... more

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4 ; Use the formula for the number of combinations... more

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7  ; Use the formula for the number of ... more

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1  ; Use the formula for the number of ... more

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1 ; Use the formula for the number of combinations... more

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40,920  ; Enter the given expression into the CAS ... more

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120 ; Enter the given expression into the CAS to ... more

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850,668 ; Enter the given expression in the CAS to... more

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15,890,700 ; Enter the given expression in the CAS... more

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AB, AC, AD, AE, AF, BC, BD, BE, BF, CD, CE, CF, DE... more

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ABC, ABD, ABE, ABF, ACD, ACE, ACF, ADE, ADF, AEF, ... more

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 approx. ; Use the formula to calculate the ... more

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190 ; Use the formula to calculate the number of ... more

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5,586,853,480 ; Use the formula to calculate the ... more

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84 ; Use the formula to calculate the number of ... more

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175,223,510 ; The number of ways in which a player... more

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1,956,240  ; The number of combinations of seven ... more

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462,000 ; The number of ways of selecting 1 ... more

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3744 ; There are 13 kinds of cards in each suit of... more

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5  ; A line segment is formed by joining two ... more

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9  ; A line segment is formed by joining two ... more

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20 ; A line segment is formed by joining two ... more

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35  ; A line segment is formed by joining two ... more

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56 ; Simplify the expressions; and in the given ... more

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 910 ; Simplify the expressions; and in the ... more

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10  ; Simplify the expressions; and in the given... more

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12  ; Simplify the expressions; and in the given... more

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3  ; Simplify the expressions; and in the given ... more

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2  ; Simplify the expressions; and in the given ... more

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2  ; Simplify the expressions; and in the given ... more

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5  ; Simplify the expressions; and in the given ... more

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False; Because order does not matter, it is an ... more

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True  ; An order of elements in a way that one ... more

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No; for some calculators, the answer is too large... more

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represents the number of ways to choose, ... more

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r-n0123451NN    2NNY   3NNYY  4NNYYY 5NNYYYYNo, ... more

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Entire Proof Answer: Apply the formula for ... more

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Entire Proof Answer: Apply the formula for ... more

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Entire Proof Answer: Apply the formula for ... more

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Entire Proof Answer: Apply the formula for ... more

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; Find the determinant, of the coefficient ... more

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approx ; Since a standard deck has 4 aces, the ... more

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0.000225 ; Let be the event representing the adult... more

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When two coins are flipped 40 times, the number of... more

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Sample space ; The set of all possible outcomes is... more

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Number of equally likely outcomes of event ; ... more

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Mutually exclusive ; Two events are said to be ... more

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Independent ; If the occurrence of one event has ... more

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; The probability of an event E is defined as the... more

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0 ; An event is said to be an impossible event if ... more

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1 ; The event whose probability is 1, is said to ... more

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The probability of two mutually exclusive events ... more

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; Since there are total 8 outcomes of tossing a ... more

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; Since there are total 8 outcomes of tossing a ... more

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; Since there are 52 cards in a standard deck of ... more

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; Since there are 52 cards in a standard deck of ... more

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; Since there are 52 cards in a standard deck of ... more

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; Since there are 52 cards in a standard deck of ... more

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; The number of outcomes obtained when a die is ... more

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; The number of outcomes obtained when a die is ... more

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; The number of outcomes obtained when a die is ... more

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; The event of tossing a six sided die twice, ... more

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; Compute the probability that the winner is ... more

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; Let be the event of choosing a winner who is ... more

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; Let be the event of choosing a winner who is ... more

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; Let be the event of choosing a winner who is ... more

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; Let be the event of drawing two red marbles. ... more

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; Let be the event of drawing two yellow marbles... more

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; Let be the event of not drawing any yellow ... more

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; Find the probability of drawing marbles of the ... more

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; Subtract the probability that the event will ... more

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; Subtract the probability that the event will ... more

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; Subtract the probability of the event hSubtract... more

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; Subtract the probability that the event will ... more

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; Subtract the probability that the event will ... more

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; Since a standard deck has 13 clubs, the ... more

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; Since a standard deck has 12 face cards,the ... more

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; Let be the event of choosing a student who is ... more

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; Let be the event of choosing a student who is ... more

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; Let be the event of choosing a student who is ... more

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; Let be the event of choosing a student who is ... more

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; Let be the event of choosing an even number. ... more

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; Consider to be an event of choosing a number, ... more

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; Let be the event of choosing a number which is ... more

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; Let be the event of choosing a number greater ... more

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; Assume 2 friends decided to meet between 5:00 ... more

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True ; Let us consider an event of obtaining a ... more

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True ; Since the events, and are independent, ... more

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There should be no common outcomes in a sample ... more

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No ; Events and are not mutually exclusive ... more

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70 ; Compute using the formula given below. ; ... more

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126 ; Compute using the formula given below. ; ... more

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165 ; Compute using the formula given below. ; ... more

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560 ; Compute using the formula given below. ; ... more

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; Compute the first term by substituting in the ... more

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; Compute the first term by substituting in the ... more

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; Compare the terms of the sequence with the ... more

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; Compare the terms of the sequence with the ... more

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; Compare the terms of the sequence with the ... more

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; Compare the terms of the sequence with the ... more

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931 ; Compute the second term of the sequence by ... more

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4955616773 ; To compute the second term of the ... more

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; Operate the factorial. ; Simplify the ... more

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90 ; Operate the factorial. ; Simplify the ... more

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; Operate the factorial. ; Simplify the ... more

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; Operate the factorial. ; To simplify the ... more

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30 ; Expand the sum from to . ; Simplify the ... more

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56 ; Expand the sum from to . ; Simplify the ... more

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; Expand the sum from to . ; Simplify the ... more

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Approx ; Expand the sum from to .  ; Simplify the... more

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Approx 1.799 ; To write the sigma notation, use 20... more

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855 ; To write the sigma notation, use 9 as the ... more

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Approx 7.07103 ; To write the sigma notation, use ... more

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0.75 ; To write the sigma notation, use infinite ... more

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Arithmetic sequence ; Compute the difference ... more

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Not an arithmetic sequence ; Compute the ... more

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Not an arithmetic sequence ; Compute the ... more

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Arithmetic sequence ; Compute the difference ... more

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    ; Substitute and in the term formula .  ; ... more

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    ; Substitute and in the term formula .  ; ... more

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    ; Relate of the arithmetic sequence with  as ... more

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; Relate of the arithmetic sequence with  as ... more

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3532292623 ; Substitute in . ; Substitute in to... more

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152025 ; Substitute in . ; Substitute in to ... more

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1600  ; Substitute and in the term formula to ... more

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2950  ; Relate of the arithmetic sequence with... more

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110 ; Expand the series. ; Notice that the common ... more

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88 ; Expand the series. ; Notice that the common ... more

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6375 ; The first 50 positive multiples of 5 are 5... more

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2440 ; The integers from 10 to 70 are 10, 11, 12... more

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630 ; The number of bales made are in arithmetic ... more

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Geometric sequence  ; Find the ratio of the second... more

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Geometric sequence  ; Find the ratio of the second... more

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Not a geometric sequence. ; To compare the ratio ... more

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Not a geometric sequence.  ; To compare the ratio ... more

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4 ; To compute the first five terms of the ... more

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23 ; To compute the first five terms of the ... more

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964 ; To compute the common ratio , divide the ... more

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212724322592 ; To compute the common ratio , ... more

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12040 ; The first term of the geometric sequence ... more

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2002020.20.02 ; The first term of the geometric ... more

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19531 ; Expand the summation of the sequence by ... more

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121 ; Expand the summation of the sequence by ... more

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9831 ; Expand the summation of the sequence by ... more

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7.5 ; Expand the summation of the sequence by ... more

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32 ; Expand the summation of the sequence by ... more

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9 ; Expand the summation of the sequence by ... more

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The series does not have a finite sum. ; Expand ... more

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; Expand the summation of the sequence by writing... more

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; Rewrite the sequence. ; To compute the common ... more

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45 ; Write the combination in factorial form. ; ... more

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792 ; Write the combination in factorial form. ; ... more

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126 ; Write the combination in factorial form. ; ... more

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91 ; Write the combination in factorial form. ; ... more

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; Calculate the binomial coefficients using ... more

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; Calculate the binomial coefficients using ... more

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; Calculate the binomial coefficients using ... more

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; Find the binomial coefficients using , where ... more

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21 ; Write the Pascal triangle. ; The third term ... more

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36 ; Form a pascal triangle.  ; The 8th term in ... more

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70 ; Form a pascal triangle.  ; The 5th term in ... more

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252 ; Form a pascal triangle. ; The 6th term in ... more

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10 ; List the choices for the first and second ... more

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180 ; Apply the Fundamental Counting Principle to ... more

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95,040 ; Use the formula for the number of ... more

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360 ; Use the formula for the number of ... more

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5040 ; The group of letters C, A, L, C, U, L, U, S... more

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90,720 ; The group of letters I, N, T, E, G, R, A... more

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; Simplify the expressions , and in the given ... more

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; Simplify the expressions , and in the given ... more

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28 ; Use the formula for the number of ... more

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1225 ; Use the formula for the number of ... more

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479,001,600 ; Calculate the number of orders in ... more

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1155 ; The number of ways in which 2 juniors can ... more

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True, as the left and the right side values are ... more

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True, as the left and the right side values are ... more

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3; 2; ; ; ; Write the first term of the sequence ... more

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   ; Substitute in . ; Substitute in to compute... more

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; ; ; ; ; Write the first term of the sequence by ... more

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; ; ; ; ; Write the first term of the sequence by ... more

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7920 ; Solve the factorial and cancel out the ... more

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; Expand each factorial. ; To simplify the ... more

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; Expand each factorial.  ; To simplify the ... more

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; Rewrite the first term in expanded form.   ; ... more

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  ; Substitute and in the term formula . ; ... more

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; Determine the common ratio of the series.  ; ... more

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189 ; Expand the series. ; Notice that the series ... more

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;  calculate the binomial coefficients using ... more

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84 ; Use the formula for the number of ... more

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1140 ; Use the formula for the number of ... more

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72 ; Use the formula for the number of ... more

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; Simplify the expressions and in the given ... more

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26,000 ; Apply the Fundamental Counting Principle ... more

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12,650 ; Use the formula to calculate the number ... more

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; Determine the number of outcomes which is the ... more

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; Determine the number of outcomes which is the ... more

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