Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 11 - Infinite Series - 11.1 Sequences - Exercises - Page 538: 45



Work Step by Step

We have $$\lim_{n\to \infty}a_n=\lim_{n\to \infty}\frac{\cos n}{{n}}.$$ Since $-1\leq \cos n\leq 1$, then $-\frac{1}{{n}}\leq \frac{\cos n}{{n}}\leq \frac{1}{{n}}$. Applying the squeeze rule, we find that $$\lim_{n\to \infty}\frac{\cos n}{{n}}=0.$$ Hence, by Theorem 1, the sequence $a_n$ converges to $0$.
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