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Thread: Recurrence Relation Q

  1. #1
    Junior Member
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    Recurrence Relation Q

    If $\displaystyle u_{n+1}=u_n+u_n^2$ and $\displaystyle u_1=\frac{1}{3}$, find $\displaystyle \sum_{n=1}^{\infty}\frac{1}{1+u_n}$.

    So far, ive gotten up to $\displaystyle \sum_{n=1}^{\infty}\frac{1}{1+u_n}=\sum_{n=1}^{\in fty}\frac{u_n}{u_{n+1}}$ but im not sure whether im on the right track.

    Can someone give me a hint on this one. Thanks
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  2. #2
    Super Member malaygoel's Avatar
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    $\displaystyle
    \frac{1}{1+u_n}=\frac{1}{u_{n}}-\frac{1}{u_{n+1}}
    $
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