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Thread: Recurrence Relation Q

  1. September 30th 2009, 06:11 PM #1
    vuze88
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    Recurrence Relation Q

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

    So far, ive gotten up to \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. September 30th 2009, 11:57 PM #2
    malaygoel
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    <br /> \frac{1}{1+u_n}=\frac{1}{u_{n}}-\frac{1}{u_{n+1}}<br />
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