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} (-1)^{n-1}\dfrac{1}{n^{p}}

, where

p

is a real parameter. For which values of

p

do the terms meet every hypothesis needed for the alternating series error bound? (a)

p\ge 1

(b)

0<p<1

(c)

p>0

(d)

p\ge 0