Consider the series

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

Problem

Consider the series

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

. Which statement best describes its behavior? (a) It converges because the ratio of successive terms is less than

1

. (b) It converges because its terms approach

0

n\to\infty

. (c) It diverges because its terms are comparable to those of the harmonic series

\displaystyle \frac{1}{n}

. (d) It converges because it can be viewed as a

p

-series with

p=3>1