bounded sequence

**serious331** · April 29th 2010, 09:13 PM

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 $\lim_{n -> \infty} {a_n . b_n}= 0$ ?

**Drexel28** · April 29th 2010, 09:48 PM

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:

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