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Math Help - more convergence help

  1. #1
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    more convergence help

    Suppose that \sum a_{k} from k=1 to infinity is a convergent series of positive numbers. Prove that the series \sum \sqrt{a_{k}a_{k+1}} from k=1 to infinity converges.
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  2. #2
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    Quote Originally Posted by friday616 View Post
    Suppose that \sum a_{k} from k=1 to infinity is a convergent series of positive numbers. Prove that the series \sum \sqrt{a_{k}a_{k+1}} from k=1 to infinity converges.
    Recall that 2ab\le a^2+b^2.

    Does it follow that 2\sqrt{a_ka_{k+1}}\le a_k+a_{k+1}?
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