Answer
Divergent
Work Step by Step
$\lim\limits_{n \to \infty}\frac{a_{n}}{b_{n}}=\lim\limits_{n \to \infty}\frac{nsin(1/n)}{n}$
$=\lim\limits_{n \to \infty}sin(\frac{1}{n})$
$=\lim\limits_{n \to \infty}sin(0)$
$=1$
The series is divergent.