For what real values of does the series converge?

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

For what real values of

p

does the series

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

converge? (a) It converges for all

p>0

. (b) It converges for

p\ge 1

and diverges for

p<1

. (c) It converges for

p>1

and diverges for

p\le 1

. (d) It does not converge for any real

p