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Math Help - [SOLVED] series convergence

  1. #1
    Junior Member
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    [SOLVED] series convergence

    Let {a}_{n}\geq 0. Prove that if

    \sum {a}_{n}

    converges, then

    \sum \frac{\sqrt{{a}_{n}}}{n}

    converges.
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  2. #2
    Senior Member
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    Use the Cauchy–Schwarz inequality on the series \sum \sqrt{a_n} and \sum \frac1n.
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  3. #3
    Junior Member
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    thanks. That does it.
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