Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 11 - Infinite Sequences and Series - Review - Exercises - Page 825: 35


$s_{6}=\Sigma_{n=1}^{6}\frac{(-1)^{n+1}}{n^{5}}\approx 0.9721$

Work Step by Step

$\Sigma_{n=1}^{\infty}\frac{(-1)^{n+1}}{n^{5}}=1-\frac{1}{32}+\frac{1}{243}-\frac{1}{1024}+...$ Since, this is an alternating series we can use alternating series estimation theorem, Here, $a_n=\frac{(-1)^{n+1}}{n^{5}}$ which means we only need to add up $a_{1}$ to $a_{6}$ $s_{6}=\Sigma_{n=1}^{6}\frac{(-1)^{n+1}}{n^{5}}\approx 0.9721$
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