Calculus (3rd Edition)

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

Chapter 11 - Infinite Series - 11.5 The Ratio and Root Tests and Strategies for Choosing Tests - Exercises - Page 568: 36


The series $\Sigma_{n=0}^{\infty} \frac{1}{10^n}$ converges.

Work Step by Step

To apply the root test, we have $$ L=\lim _{n \rightarrow \infty} \sqrt[n]{a_{n}}=\lim _{n \rightarrow \infty} \sqrt[n]{1/10^n}=1/10\lt 1 $$ Hence the series $\Sigma_{n=0}^{\infty} \frac{1}{10^n}$ converges.
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