Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 10: Infinite Sequences and Series - Section 10.2 - Infinite Series - Exercises 10.2 - Page 580: 54



Work Step by Step

Formula to calculate the sum of a geometric series is:$S=\dfrac{a}{1-r}$ Consider the series $\lim\limits_{n \to \infty} \cos \pi n= (-1)^n$ with first term, $a=1$ and common ratio $r =\dfrac{-1}{5}$ Hence, $S=\dfrac{a}{1-r}=\dfrac{1}{1-(\dfrac{-1}{5})}$ or $S=\dfrac{5}{6}$
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