Let be a real number

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

Problem

Let

k

be a real number. Determine all

k

for which the series

\sum_{n=1}^{\infty}\frac{n^{2}+n^{k}}{n^{k+3}}

converges. (a) It converges if and only if

k<-2

. (b) It converges if and only if

k>0

. (c) It converges for all real

k

.},{ (d) It converges if and only if

k\ge 0