Consider the series

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Consider the series

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

. Which of the two required conditions for using the alternating-series error bound—(i)

|a_{n}|\to 0

and (ii)

|a_{n}|

is monotonically decreasing—fails for this series, and why?