# Comparison or Limit Comparison Test Problem

• Mar 12th 2010, 01:45 AM
crymorenoobs
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.
• Mar 12th 2010, 06:49 AM
Plato
Quote:

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 $\left( {\ln (n)} \right)^{\ln (n)} = n^{\ln \left[ {\ln (n)} \right]} ?$
• Mar 12th 2010, 07:46 AM
Miss
@Plato: it should be n not x.