For , consider the series _ n=2 ^ (-1)^ n-1 n n^ p , where is a positive constant.…

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

Problem

For

n\ge 2

, consider the series

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

where

p

is a positive constant. For which of the following values of

p

does the series converge conditionally but not absolutely? (a)

p=\dfrac{3}{2}

(b)

p=\dfrac{4}{3}

(c)

p=\dfrac12

(d)

p=2