## Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning

# Chapter 11 - Section 11.7 - Strategy for Testing Series - 11.7 Exercises - Page 746: 32

Divergent

#### Work Step by Step

$\lim\limits_{n \to \infty}\sqrt[n] a_{n}=\lim\limits_{n \to \infty}\sqrt[n] {(\frac{n!}{n^{4}})^{n}}$ $=\lim\limits_{n \to \infty}\frac{n!}{n^{4}}$ $=\infty \gt 1$ The series is divergent by the root test.

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