Explanation Given: The given sum is: ∑ k = 1 n ( k 3 − 10 k 2 + 2 ) Calculation: The sum can be written as = ∑ k = 1 n ( k 3 − 10 k 2 + 2 ) = ∑ k = 1 n k 3 − ∑ k = 1 n 10 k 2 + 2 ∑ k = 1 n 1 = n 2 ( n + 1 ) 2 4 − 10 ( n ( n + 1 ) ( 2 n + 1 ) 6 ) + 2 n The value for n = 100 will be = n 2 ( n + 1 ) 2 4 − 10 ( n ( n + 1 ) ( 2 n + 1 ) 6 ) + 2 n = ( 100 ) 2 ( 100 + 1 ) 2 4 − 10 ( 100 ( 100 + 1 ) ( 2 ( 100 ) + 1 ) 6 ) + 2 ( 100 ) = 10000 ( 10201 ) 4 − 5 ( 10100 ) ( 201 ) 3 + 200 = 25502500 − 3383500 + 200

14th Edition

ISBN: 9781464140051

Author: TAALMAN, Laura, Kohn, Peter

Publisher: W. H. Freeman

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Chapter 4.1, Problem 36S

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The formula for the sums and the value for n = 100, n = 500 and n = 1000

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Chapter 4.1, Problem 35S

Chapter 4.1, Problem 37S

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find the zeros of the function algebraically: f(x) = 9x2 - 3x - 2

Chapter 4 Solutions

Loose-leaf Version for Calculus

Ch. 4.1 - Prob. 1TB Ch. 4.1 - Prob. 2TB Ch. 4.1 - Prob. 3TB Ch. 4.1 - Prob. 0C Ch. 4.1 - Prob. 1C Ch. 4.1 - Prob. 2C Ch. 4.1 - Prob. 3C Ch. 4.1 - Prob. 4C Ch. 4.1 - Prob. 5C Ch. 4.1 - Prob. 6C

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ACP Ch. 4 - Prob. BCP Ch. 4 - Prob. CCP Ch. 4 - Prob. DCP

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The formula for the sums and the value for n = 100, n = 500 and n = 1000

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The formula for the sums and the value for n = 100, n = 500 and n = 1000

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Chapter 4 Solutions