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Math Help - [SOLVED] Infinite series proof.

  1. #1
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    [SOLVED] Infinite series proof.

    If \sum ^\infty _{n=1} a_n converges and a_n>0, \forall n \in \mathbb{N} , than does  \sum ^\infty _{n=1} \frac{\sqrt{a_n}}{n} converges??

    I think it converges, but I don't know if I am right, or how to prove it.
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  2. #2
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    Quote Originally Posted by akolman View Post
    If \sum ^\infty _{n=1} a_n converges and a_n>0, \forall n \in \mathbb{N} , than does  \sum ^\infty _{n=1} \frac{\sqrt{a_n}}{n} converges??

    I think it converges, but I don't know if I am right, or how to prove it.
    Geometric-arithmetic mean inequalty: \left(a_nn^{-2}\right)^{1/2}\leqslant\tfrac12\left(a_n+n^{-2}\right).
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