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Math Help - algebraic fraction problem real one

  1. #1
    Junior Member
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    algebraic fraction problem real one

    Sum the series:

    a1 + a2 + .... + a99

    where an =
    1
    __________________________
    (n+1)sqrt(n)+nsqrt(n+1)

    For n = 1,2,...99

    BTW THE LETTERS/NUMBERS ON RED ARE MEANT TO BE IN SUBSCRIPT
    the sqrt in blue represents a square root sign for whatever follows it in brackets
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  2. #2
    MHF Contributor red_dog's Avatar
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    Medgidia, Romania
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    \frac{1}{(n+1)\sqrt{n}+n\sqrt{n+1}}=\frac{1}{\sqrt  {n}\sqrt{n+1}(\sqrt{n+1}+\sqrt{n})}=

    =\frac{\sqrt{n+1}-\sqrt{n}}{\sqrt{n}\sqrt{n+1}}=\frac{1}{\sqrt{n}}-\frac{1}{\sqrt{n+1}}

    Now, replace n with 1, 2, 3,....,99.
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