Let be a real number

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

Problem

Let

p

be a real number. Consider the series

\displaystyle \sum_{n=2}^{\infty} (-1)^{n-1}\frac{(\ln n)^{p}}{n}

. For which values of

p

does this series converge absolutely? (a)

p\le -1

(b)

p<0

(c)

p<-1

(d)

p>-1