For the series

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

Problem

For the series

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

, classify the convergence in terms of

p

: give the set of

p

for which the series is absolutely convergent, the set for which it is conditionally convergent, and the set for which it diverges.