Determine which statement correctly describes the convergence of the series _ n=1 ^…

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

Problem

Determine which statement correctly describes the convergence of the series

\sum_{n=1}^{\infty}\frac{2n^{k}+7}{n^{k+4}}

for real values of

k

. (a) The series converges only when

k>-4

. (b) The series converges for every real value of

k

. (c) The series converges only when

k>-3

. (d) The series converges only when

k>1