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-1}\dfrac{n}{n+1}

. Which of the following two requirements fails for this series: (i)

\{b_n\}

is eventually non-increasing, or (ii)

\displaystyle \lim_{n\to\infty} b_n = 0

? Briefly justify your choice and state whether the series converges or diverges.