$\sum_{n=1}^{\infty} 1/\sqrt[n]{n}$ converge Does the series:
$$
\sum_{n=1}^{\infty} \frac{1}{\sqrt[n]{n}}
$$
converge or diverge?
I'm unsure where to start with this question. I know that $n$th root of $n$ converges to $1$ but not sure about its reciprocal. 

If a series $\sum_{n=0}^\infty a_n$ converges, then $\lim_na_n=0$. Therefore your series diverges.
