Mathematics

Mathematics

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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