## Calculus (3rd Edition)

Published by W. H. Freeman

# Chapter 11 - Infinite Series - Chapter Review Exercises - Page 592: 75

#### Answer

The series $\sum_{n=1}^{\infty} (3/4n)^n$ converges.

#### Work Step by Step

To apply the root test, we have $$L=\lim _{n \rightarrow \infty} \sqrt[n]{a_{n}}=\lim _{n \rightarrow \infty} \sqrt[n]{(3/4n)^n}=\lim _{n \rightarrow \infty} \frac{3}{4n}=0\lt 1$$ Hence the series $\sum_{n=1}^{\infty} (3/4n)^n$ converges.

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