Help with proving if $s_n$ converges to $0$ and $x_n$ is a bounded sequence, then $\lim(x_ns_n)=0$ 
Prove: If $s_n$ converges to $0$ and $x_n$ is a bounded sequence, then $\underset{n \to \infty}{\lim}(x_ns_n)=0$

I'm have trouble getting started on this proof.  
Since I know $s_n$ converges to $0$ I feel like I should start using the epsilon definition with $x_n$ 
Since $\underset{n \to \infty}{\lim} s_n=0$
So $\left|x_n-s_n\right| \lt \epsilon \implies (=) \quad \left|x_n\right| \lt \epsilon$
But I'm not sure if the aforementioned steps are correct and where to go from here.

HINT: If $x_n$ is bounded, then $\exists M>0: |x_n|<M$ for all $n$. Hence $|x_ns_n|<M\varepsilon$ for large $n$. It should be clear that $x_ns_n$ also tends to 0.
