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Math Help - Convergence of series

  1. #1
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    Convergence of series

    I am having a hard time proving this result. Could someone give me a hand? Thanks.
    If \sum {a_n}^2 and \sum {b_n}^2 converge, then \sum a_n b_n converges absolutely.
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  2. #2
    GJA
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    Re: Convergence of series

    Hi jackie,

    I think we can get what you're looking for using the Cauchy-Schwarz inequality. Give it a shot with this and let me know how it goes. Good luck!
    Thanks from jackie
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  3. #3
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    Re: Convergence of series

    Thank you for your help GJA. By using the Cauchy-Schwarz inequality I am able to get a bound for the sequence of partial sums of the series \sum \mid a_n b_n \mid. Clearly, the sequence of partial sums is increasing. That should be enough to show convergence right?
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