Consider the series

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

Problem

Consider the series ∑n=1∞3n+5n2+n\displaystyle \sum_{n=1}^{\infty}\frac{3n+5}{n^{2}+n}. Which of the following best describes its behavior? (a) It converges, because its terms behave like those of a pp-series with p>1p>1. (b) It diverges, because its terms do not approach zero. (c) It diverges, because its terms behave like those of the harmonic series. (d) It converges by the Ratio Test since lim⁡n→∞an+1an<1\displaystyle \lim_{n\to\infty}\frac{a_{n+1}}{a_n}<1.

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