Answer
Converges to $0$
Work Step by Step
Consider $\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty} n (1-\dfrac{1}{n})$
But $\lim\limits_{n \to \infty} n (1-\dfrac{1}{n})=\dfrac{0}{0}$
Need to apply L-Hospital's rule.
So, $ \lim\limits_{n \to \infty} \dfrac{\sin (1/n) \cdot (1/n^2)}{\dfrac{1}{n^2}}=\lim\limits_{n \to \infty} \sin (\dfrac{1}{n})$
or, $=0$
Hence, $\lim\limits_{n \to \infty} a_n=0$ and {$a_n$} is Convergent and converges to $0$
