# Homework Help: Convergence? (analysis)

1. Sep 21, 2007

### steviet

$$\sum_{n=1}^\infty \frac{1}{n\sqrt[n]{n}}\]$$

Does this series converge?

2. Sep 21, 2007

### Gib Z

No it doesn't, because $$\sqrt[n]{n}}$$ approaches 1 as n approaches infinity. Hence if we were to the the first k partial sums of the series in your post, and the harmonic series, the difference would approach a constant as k approached infinity. Since the harmonic series diverges, so does this one.