# Convergence of a series

#### dwsmith

##### Well-known member
$\sum\limits_{n = 2}^{\infty}\frac{1}{(\ln n)^{\ln n}}$

I am trying to show that this series diverges or converges

#### Opalg

##### MHB Oldtimer
Staff member
$\sum\limits_{n = 2}^{\infty}\frac{1}{(\ln n)^{\ln n}}$

I am trying to show that this series diverges or converges
Hint: $\displaystyle\frac{1}{(\ln n)^{\ln n}} = \frac{1}{e^{\ln n \ln(\ln n)}}$, and if $n$ is large enough then $\ln(\ln n)>2$.