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Math Help - Sequence proof

  1. #1
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    Sequence proof

    Let (a_{n}) be a sequence which converges to 0, and let (b_{n}) be a sequence which is bounded but not necessarily convergent.

    Prove that lim (a_{n})(b_{n}) = 0

    No idea what to do here.
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  2. #2
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    Well I am not so sure about this but cant you do something in this direction?

    If b_n is bounded then there exists M such that
    <br />
|b_n|\leq M <br />
    For all n\in \mathbb{N}

    Now then it is clear that:
    <br />
\lim\limits_{n\to\infty}(a_n)(-M) \leq \lim\limits_{n\to\infty}(a_n)(b_n) \leq \lim\limits_{n\to\infty}(a_n)M<br />

    <br />
0\leq\lim\limits_{n\to\infty}(a_n)(b_n)\leq 0<br />

    Something like this?
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  3. #3
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    I figured the squeeze theorem would show up in this one. I am horrible at generalizing like that. Thanks
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  4. #4
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    Not a problem, I am not so good either.
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