If we have $\displaystyle \lim_{n -> \infty} {a_n} = 0$,and another sequence $\displaystyle b_n$ that is bounded, how can we show that $\displaystyle \lim_{n -> \infty} {a_n . b_n}= 0$

I tried supposing $\displaystyle b_n = (-1)^n$, which is a bounded sequence, but it does not converge!

then, how does $\displaystyle \lim_{n -> \infty} {a_n . b_n}= 0 $?