Consider the family of series

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

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

, where

p

is a real parameter. Identify all values of

p

for which the series converges absolutely, converges conditionally, and diverges.