# Thread: Test the series convergence

1. ## Test the series convergence

this is a hard one
I tried many times
and I always failed
here is it:

$\displaystyle \sum_{n=2}^{\infty} \frac{1}{ln^e \, (n)}$

2. Originally Posted by TWiX
this is a hard one
I tried many times
and I always failed
here is it:

$\displaystyle \sum_{n=2}^{\infty} \frac{1}{ln^e \, (n)}$

There always exists $\displaystyle N_k\in\mathbb{N}\,\,\,s.t.\,\,\,n>N_k\Longrightarr ow \ln^k(n)<n$ , no matter what $\displaystyle k\in\mathbb{N}$ is, so...

Tonio