University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 9 - Section 9.2 - Infinite Series - Exercises - Page 498: 54



Work Step by Step

The sum of a geometric series can be found as: $S=\dfrac{a}{1-r}$ The given series $\lim\limits_{n \to \infty} \cos \pi n= (-1)^n$ has first term, $a=1$ and common ratio $r =\dfrac{-1}{5}$ Thus, $S=\dfrac{1}{1-(\dfrac{-1}{5})}=\dfrac{5}{6}$
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