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: 53



Work Step by Step

The function $\cos x$ always oscillates in between $-1$ and $+1$. This implies that it does not have any limit and lso, $\cos \pi n=1$; for even value of $n$ and $\cos \pi n=-1$; for odd values of $n$ Thus, $\lim\limits_{n \to \infty} \cos \pi n$= Limit does not exist or divergent. Hence, the series diverges.
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