Determine whether the series _ n=1 ^ 4n^ 2 -1 3n^ 3 +2 converges or diverges.

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

Problem

Determine whether the series

\sum_{n=1}^{\infty}\frac{4n^{2}-1}{3n^{3}+2}

converges or diverges. (a) It converges because its terms behave like

\dfrac{1}{n^{2}}

. (b) It converges because its terms approach

0

. (c) It diverges because its terms behave like

\dfrac{1}{n}

. (d) It converges because it is a

p

-series with

p=3>1