For which real values of does the series _ n=1 ^ n^ k n^ 2 +n^ k converge?

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

Problem

For which real values of

k

does the series

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

converge? (a) It converges if and only if

k\le 0

. (b) It converges if and only if

-1<k<1

. (c) It converges if and only if

k<1

. (d) It converges if and only if

k>1