# Chapter 9 - Section 9.2 - Infinite Series - Exercises - Page 497: 31

Diverges

#### Work Step by Step

Given: $\Sigma_{n =1}^{\infty} \cos \dfrac{1}{n}$ Since the function $\cos x$ is continuous at $0$, we have: $\lim\limits_{n \to \infty} \dfrac{1}{n}=0$ and $\cos \lim\limits_{n \to \infty} \dfrac{1}{n}=\cos (0)=1\ne 0$ Hence, the series is divergent.

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