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Math Help - Summing Infinite Series Questions

  1. #1
    Junior Member CuriosityCabinet's Avatar
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    Summing Infinite Series Questions

    How to sum this series?

    \sum_{n=0}^{\infty} \left( \left(\frac{1}{2}+\frac{1}{\sqrt{5}}\right)^n + \left(\frac{1}{2}-\frac{1}{\sqrt{5}}\right)^n \right)
    Last edited by CuriosityCabinet; August 30th 2010 at 11:10 AM.
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  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Note that

    \displaystyle \sqrt{5}>2 \implies \frac{1}{2}\pm \frac{1}{\sqrt{5}}<1

    So just break the the series into two parts they are both geometric and remember that

    \displaystyle \sum_{n=0}^{\infty}r^n=\frac{1}{1-r}
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  3. #3
    Junior Member CuriosityCabinet's Avatar
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    Thank you very much, the answer came out to be 20
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