For which set of real values of (p ) does the series ( _ n=1 ^ (-1)^ n n^ p e^ n )…

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

Problem

For which set of real values of

p

does the series

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

converge? (a) Only

p<0

(b) Only

p>0

p

(d) Only

-1<p<1