Answer
Converges
Work Step by Step
Let us consider $a_n=(\dfrac{1}{n}-\dfrac{1}{n^2})^n$
Apply Root Test.
$L=\lim\limits_{n \to \infty} \sqrt [n] {|a_n|}=\lim\limits_{n \to \infty} |a_n|^{1/n}$
This test states that when $L \lt 1$; the series converges and when $L \gt 1$ then the series diverges.
$l=\lim\limits_{n \to \infty} \sqrt [n] {|a_n|}=\lim\limits_{n \to \infty}\sqrt [n] {|(\dfrac{1}{n}-\dfrac{1}{n^2})^n|}$
$\implies L=\lim\limits_{n \to \infty}(\dfrac{1}{n}-\dfrac{1}{n^2})=0 \lt 1$
Hence, the series converges by the Root Test.