Determine the value of and state whether the series converges or diverges based on…

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

Problem

Determine the value of

\displaystyle\lim_{n\to\infty} n\sin\!\left(\tfrac{1}{n}\right)

and state whether the series

\displaystyle\sum_{n=1}^{\infty} n\sin\!\left(\tfrac{1}{n}\right)

converges or diverges based on that limit.