## Calculus (3rd Edition)

Published by W. H. Freeman

# Chapter 11 - Infinite Series - 11.5 The Ratio and Root Tests and Strategies for Choosing Tests - Exercises - Page 568: 1

#### Answer

The series converges.

#### Work Step by Step

We have to calculate $\rho$: $$\rho=\lim _{n \rightarrow \infty}\left|\frac{a_{n+1}}{a_{n}}\right|=\lim _{n \rightarrow \infty}\left|\frac{1/5^{(n+1)}}{1/5^n}\right|=1/5 \lt 1$$ Thus the series converges.

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