Answer
The sequence converges to zero.
Work Step by Step
Given
$$a_{n} = \frac{\sin(n)}{n}$$
$$-1 \leq \sin(n) \leq 1$$
Then
\begin{aligned}
-\frac{1}{n} \leq \frac{\sin(n)}{n} \leq \frac{1}{n}
\end{aligned}
Since
\begin{aligned}
\lim\limits_{n \to ∞}\left(-\frac{1}{n}\right) = 0
\end{aligned}
and
\begin{aligned}
\lim\limits_{n \to ∞}\frac{1}{n} = 0
\end{aligned}
By the Squeeze Theorem, we have
$$\lim\limits_{n \to ∞}\frac{\sin(n)}{n} = 0$$
Therefore, the sequence converges to $0$.
