calculus - Convergence of $sum_{n=0}^infty n^{1/n}-1$ and $sum_{n=0}^infty (1/n!)^{1/n}$

$$\sum_{n=0}^\infty n^{1/n}-1$$
$$\sum_{n=0}^\infty (1/n!)^{1/n}$$

Hi. I am working on calculus now. While studying convergence test part, I ran into those problems... Wolfram alpha says they both diverges by comparison test. But I cannot think of the series to apply the comparison test... I tried $\sum 1/n$ or $\sum 1/n^2$ but failed..... Can you give me any clue?? I'd really appreciate your help.