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Math Help - Absolute Convergence Question

  1. #1
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    Absolute Convergence Question


    I tried using the definition of absolute convergence (similar to Cauchy Criterion), but had trouble reaching at ajbj.
    Any help would be greatly appreciated.
    Thanks
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  2. #2
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    Krizalid's Avatar
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    apply the Cauchy-Schwarz inequality.
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  3. #3
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    I understand


    but how do I get rid of the square signs on sequence a and b?
    I can't make a connection
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  4. #4
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    Here's what I just tried.



    but the absolute sign is around the whole summation, not just the term.
    Am I doing this right?
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  5. #5
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    i wasn't actually talking about that kind of application, what i meant is \sum\limits_{j=1}^{\infty }{a_{j}b_{j}}\le \sqrt{\sum\limits_{j=1}^{\infty }{a_{j}^{2}}\cdot \sum\limits_{j=1}^{\infty }{b_{j}^{2}}}.

    (ohhh, may be it's the same, it's just that i'm not so familiar with norms.)
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