Answer
Converges
Work Step by Step
Consider $a_n=(\dfrac{1}{n}-\dfrac{1}{n^2})^n$
By the Root Test $l=\lim\limits_{n \to \infty} \sqrt [n] {|a_n|}=\lim\limits_{n \to \infty} |a_n|^{1/n}$
$l=\lim\limits_{n \to \infty} \sqrt [n] {|a_n|}=\lim\limits_{n \to \infty}\sqrt [n] {|(\dfrac{1}{n}-\dfrac{1}{n^2})^n|}=\lim\limits_{n \to \infty}(\dfrac{1}{n}-\dfrac{1}{n^2})$
or, $=0$
So, $l=0 \lt 1$
Thus, the given series Converges by the Root Test.