Answer
$0$
Work Step by Step
We have
$$\lim_{n\to \infty}a_n=\lim_{n\to \infty}\frac{\cos n}{{n}}.$$
Since $-1\leq \cos n\leq 1$, then $-\frac{1}{{n}}\leq \frac{\cos n}{{n}}\leq \frac{1}{{n}}$. Applying the squeeze rule, we find that $$\lim_{n\to \infty}\frac{\cos n}{{n}}=0.$$
Hence, by Theorem 1, the sequence $a_n$ converges to $0$.
