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 497: 34


The limit does not exist or diverges.

Work Step by Step

The value of the function $\cos x$ always oscillates in between $-1$ and $+1$. Thus, its acquires no limit and $\cos \pi n=1$ for even values of $n$ and $\cos \pi n=-1$; for odd values of $n$. Therefore, $\lim\limits_{n \to \infty} \cos \pi n$= Limit does not exist Hence, the series is divergent.
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