Consider the series _ n=2 ^ n^ k +5 n^ k+1 n

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

Problem

Consider the series

\sum_{n=2}^{\infty}\frac{n^{k}+5}{n^{k+1}\ln n}.

For which real values of

k

does this series converge? (a) It converges if and only if

k>0

. (b) It converges for all real

k

. (c) It diverges for all real

k

. (d) It converges if and only if

k<-1