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Math Help - bounded sequence

  1. #1
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    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 ?
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by serious331 View Post
    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

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