Check whether or not $\sum_{n=1}^{\infty}{1\over n\sqrt[n]{n}}$ converges. Check whether or not $\sum_{n=1}^{\infty}{1\over n\sqrt[n]{n}}$ converges.  
I tried few things but it wouldn't work out. I would appreciate your help.

$\require{cancel}$
Using the limit comparison test with the harmonic series we see
$$\lim_{n\to\infty} {\cancel{(1/n)}\cdot 1\over \cancel{(1/n)}\sqrt[n]{n}}=1$$
hence the series diverges since the harmonic series does.
