Mathematics

Mathematics

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

.

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