# Math Help - Is the series covergent or divergent?

1. ## Is the series covergent or divergent?

Hi!

Problem: $\sum_{k=1}^{\infty} (\sqrt[k]{k}-1)$ , convergent or divergent?

Thx

2. Use $x>\ln(1+x)$ for $x>0$ with $x=\root k\of k-1$. Then $\root k\of k-1>\ln(\root k\of k)=\frac{\ln k}k$.

By comparison with $\sum\frac1k$ the series diverges.

3. That is clever!