Mathematics

Problem

Determine whether the series

\displaystyle \sum_{n=1}^{\infty} \frac{n}{n^{2}+5}

converges or diverges. a) It converges because its terms are eventually dominated by

\displaystyle \frac{1}{n^{2}}

. b) It converges because the series' terms approach

0

n\to\infty

. c) It diverges because its terms are comparable to

\displaystyle \frac{1}{n}

. d) It converges because the integral

\displaystyle \int_{1}^{\infty} \frac{n}{n^{2}+5}\,dn

is finite.