Determine for which real values of the series converges.

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

Problem

Determine for which real values of

p

the series

\displaystyle\sum_{n=1}^{\infty}\dfrac{1}{n^{p}}

converges. (a) It converges only when

p\ge 1

. (b) It converges for all

p>0

. (c) It converges only when

p>1

. (d) It converges only when

0<p<1