Mathematics

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