Which statement best justifies that the series converges?

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

Problem

Which statement best justifies that the series

\displaystyle\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{n}

converges? (a) Its terms form a

p

\!-series with

p>1

. (b) The absolute value of the ratio of successive terms is constant and less than

1

. (c) Its terms decrease in magnitude to

0

and alternate in sign. (d) The series of absolute values

\displaystyle\sum_{n=1}^{\infty}\frac{1}{n}

converges, so the alternating series converges.