Is the following series converging $\sum_{n=2}\dfrac{1}{(\ln n)^{\ln n}}$ Is the following series converging $\sum_{n=2}\dfrac{1}{(\ln n)^{\ln n}}$
I am not able to compare this with anything, can some show the way 

HINT:
L'Hospitals rule gives us$$\lim_{n\to \infty}\dfrac{\ln n}{n}=0.$$ Therefore $$2\le\ln n\le n$$ for sufficiently large $n$ values. This implies $$\dfrac{1}{\ln n^{\ln n}}\le\dfrac{1}{n^2}.$$ I'm sure you can continue from here.
