For which values of the real parameter does the series converge?

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

Problem

For which values of the real parameter

p

does the series

\displaystyle\sum_{n=1}^{\infty}\frac{n}{n^{p}+1}

converge? (a) It converges for

p\ge 2

. (b) It converges for

p>2

. (c) It converges for

p>1

. (d) It converges for

p>0