It looks like you already have it! You wrote down . This is precisely , which diverges.
I need to determine, using the Cauchy Condensation Test, whether or not
the series 1/(n * Log(n)) converges. I believe that this series converges iff
2^n(1/(2^n*Log(2^n)) converges and I believe that it actually diverges. But I am not sure how to work through it. Thanks for your help.