Math Help - One more series problem

1. One more series problem

This one I'm not sure how to go about. The series is the sum from 1 to infinity of:

$n/(ln(n))^n$

Just from looking at it I'm assuming it converges, but how do I prove it?

2. Originally Posted by Tbone456
This one I'm not sure how to go about. The series is the sum from 1 to infinity of:

$n/(ln(n))^n$

Just from looking at it I'm assuming it converges, but how do I prove it?
Try the Root Test if $\lim\sqrt[n]{|a_n|}<1$ then the series converges, find $\lim\sqrt[n]{\frac{n}{\ln^n(n)}}$

3. Originally Posted by Mathstud28
Try the Root Test if $\lim\sqrt[n]{|a_n|}<1$ then the series converges, find $\lim\sqrt[n]{\frac{n}{\ln^n(n)}}$
Ok, so with some simplification I assume that ends up going to zero since the ln(n) in the denominator goes to infinity. Thanks!