For which real values of does the series converge?

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

Problem

For which real values of

p

does the series

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

converge? (a) It converges exactly when

p\ge 1

. (b) It converges for all

p>0

. (c) It converges exactly when

p>1

. (d) It converges exactly when

p<-1