Consider the series

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

Problem

Consider the series

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

, where

p

is a real constant. For which values of

p

does the series converge conditionally (that is, it converges but not absolutely)? (a)

p>1

(b)

p>0

(c)

0<p\le 1

(d)

0<p<1