Answer
Diverges
Work Step by Step
Let $u_n=\dfrac{1}{(n) (\sqrt[n] n)}$ and $v_n=(\dfrac{1}{n})$
Now, $\lim\limits_{n \to \infty}\dfrac{u_n}{v_n} =\lim\limits_{n \to \infty}\dfrac{\dfrac{1}{(n) (\sqrt[n] n)}}{1/n}$
$ \implies \lim\limits_{n \to \infty} \dfrac{1}{\sqrt[n] n}=\lim\limits_{n \to \infty} \dfrac{1}{n^{(1/n)}}$
and $\dfrac{1}{1}=1 \ne 0 \ne \infty $
Hence, the series diverges by the limit comparison test.