Determine the convergence classification of the series .

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

Problem

Determine the convergence classification of the series

\displaystyle \sum_{n=1}^{\infty} (-1)^n\dfrac{n}{3^n}

. (a) The series converges conditionally but not absolutely. (b) The series diverges because

\displaystyle\lim_{n\to\infty}\frac{n}{3^n}\neq0

. (c) The series converges absolutely. (d) The series diverges by the

p

-series test with

p=1