# Thread: Comparison or Limit Comparison Test Problem

1. ## Comparison or Limit Comparison Test Problem

I need to make a suitable comparison or limit comparison to determine whether

(sum from n=2 to infinity of) (1/(ln n)^(ln n))

converges or diverges. I know it converges but cannot find a suitable comparison to show this with.

2. Originally Posted by crymorenoobs
I need to make a suitable comparison or limit comparison to determine whether
(sum from n=2 to infinity of) (1/(ln n)^(ln n))
converges or diverges. I know it converges but cannot find a suitable comparison to show this with.
Hint: Can you prove that $\left( {\ln (n)} \right)^{\ln (n)} = n^{\ln \left[ {\ln (n)} \right]} ?$

3. @Plato: it should be n not x.