Mathematics

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.