# Math Help - bounded sequence

1. ## bounded sequence

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

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

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

2. Originally Posted by serious331
If we have $\lim_{n -> \infty} {a_n} = 0$,and another sequence $b_n$ that is bounded, how can we show that $\lim_{n -> \infty} {a_n . b_n}= 0$

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

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

Spoiler:

Squeeze theorem