Calculus (3rd Edition)

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

Chapter 11 - Infinite Series - Chapter Review Exercises - Page 592: 73


The series $\sum_{n=1}^{\infty} \frac{1}{4^n}$ converges.

Work Step by Step

To apply the root test, we have $$ L=\lim _{n \rightarrow \infty} \sqrt[n]{a_{n}}=\lim _{n \rightarrow \infty} \sqrt[n]{1/4^n}=1/4\lt 1 $$ Hence the series $\sum_{n=1}^{\infty} \frac{1}{4^n}$ converges.
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