Find the values of p for which the series Sigma(1 / ( n (ln n) [ln(ln n)]^p )) is convergent.?

Question

I understand that n n < ln (n) < n^2 and that n^p is convergent if p > 1. Where do I proceed from there?

Answer 1

Use Integral Test. To do the integral, use the substitution u = ln(ln(x))