Consider the series ( _ n=1 ^ (-1)^ n+1 n^ p n^ p +1 )

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}\frac{n^{p}}{n^{p}+1}

. For which of the following describes the set of all real

p

that produce convergence? (a)

p>0

(b)

p<-1

(c)

p<0

(d)

-1<p<1