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