For the series with

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

Problem

For the series

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

with

p>0

, which of the following statements is true? (a) It converges absolutely for

p\ge 1

and conditionally for

0<p<1

. (b) It converges absolutely for

p>1

and conditionally for

0<p\le 1

. (c) It converges absolutely for

p>2

and conditionally for

1<p\le 2

. (d) It converges conditionally for

0<p<1

and diverges for

p\ge 1