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: Our denominator is $\exp((\ln\ln n)(\ln n))$, which is $n^{\ln\ln n}$. Now think $p$-series and Comparison.
Remark: When we meet $a^b$, the fact that it is equal to $\exp((\ln a)(b))$ is frequently useful. 
