# Chapter 11 - Section 11.6 - Absolute Convergence and the Ratio and Root Tests - 11.6 Exercises - Page 743: 18

The series is absolutely convergent.

#### Work Step by Step

Ratio Test: $\lim\limits_{n \to \infty}|\dfrac{a_{n+1}}{a_{n}}|=\lim\limits_{n \to \infty}|\dfrac{\frac{(n+1)!}{(n+1)^{n}}}{\frac{n!}{n^{n}}}|$ $=\lim\limits_{n \to \infty}|[\frac{n}{n+1}]^{n}|$ $=\lim\limits_{n \to \infty}|[\frac{1}{1+1/n}]^{n}|$ $=\frac{1}{e}\lt 1$ The series is absolutely convergent.

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.