Mathematics

Problem

The series

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

is under consideration. What does the

n

th-term test alone reveal about this series? a) It converges because the limit of its terms is

0

.},{ b) It diverges because the limit of

\displaystyle\frac{(-1)^n}{n}

does not exist. c) It yields no conclusion because

\displaystyle\lim_{n\to\infty}\frac{(-1)^{n}}{n}=0

. d) It converges because the terms alternate in sign and decrease in magnitude.