For which real values of does the series converge

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

For which real values of

p

does the series

\displaystyle \sum_{n=2}^{\infty} \frac{1}{n(\ln n)^{p}}

converge? State the set of all such

p

with a brief justification.