## Calculus 8th Edition

Published by Cengage

# Chapter 11 - Infinite Sequences and Series - Review - True-False Quiz: 8

TRUE

#### Work Step by Step

Ratio Test: $\lim\limits_{n \to +\infty}|\frac{a_{n}+1}{a_{n}}|=\lim\limits_{n \to +\infty}|\frac{1}{n+1!}\times \frac{n!}{1}|$ Here, $\frac{1}{n+1!}$ can also written as $\frac{1}{n+1!}=\frac{1}{n!}\times \frac{1}{n+1}$ Therefore, $\lim\limits_{n \to +\infty}|\frac{a_{n+1}}{a_{n}}|=\lim\limits_{n \to +\infty}|\frac{1}{n+1}|=0$ So, the given series converges by Ratio Test when limit equals $0$ which is $\lt 1$ . Hence, the statement is TRUE.

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