Mathematics

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