## Calculus: Early Transcendentals 8th Edition

$\sum_{n=1}^{\infty}a_{n}=\sum_{n=1}^{\infty}\frac{(-2)^n}{n^n}$ $|a_{n}|=\frac{2^n}{n^n}=(\frac{2}{n})^{n}$ $\lim\limits_{n \to \infty} \sqrt[n] |a_{n}|=\lim\limits_{n \to \infty} \sqrt[n] {(\frac{2}{n})^{n}}$ $=\lim\limits_{n \to \infty} {\frac{2}{n}}$ $=0\lt 1$ The series is absolutely convergent by root test.