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{3n+2}{n}

. Which statement is most consistent with the behavior of its terms as

n\to\infty

? (a) The series converges because its terms approach

0

. (b) The series converges because the numerator grows slower than the denominator. (c) The series diverges because its terms approach

3

. (d) The series diverges because the ratio test gives

\displaystyle\lim_{n\to\infty}\frac{a_{n+1}}{a_n}=3