Answer
Converges
Work Step by Step
Given
$$\sum_{n=1}^{\infty}\frac{1}{n^n}$$
By using the Root Test, we get:
\begin{align*}
\rho&=\lim _{n \rightarrow \infty}\sqrt[n]{a_{n}}\\
&=\lim _{n \rightarrow \infty}\sqrt[n]{ \frac{1}{n^n}}\\
&= \lim _{n \rightarrow \infty}\frac{1}{n}\\
&=0<1
\end{align*}
Thus the series converges.
