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Math Help - Continued fraction for sqrt(e)

  1. #1
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    Continued fraction for sqrt(e)

    Hi all,

    Can anyone point me towards a proof that the continued fraction expansion of sqrt(e) is [1,1,1,1,5,1,1,9,1,1,13...] (ie. a proof that the pattern continues)? I can find plenty for e itself but none for the square root.

    Thanks!
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  2. #2
    Junior Member ignite's Avatar
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    Re: Continued fraction for sqrt(e)

    Here you can find proof for continued fraction of e^\frac{2}{k} :
    JSTOR:The Simple Continued Fraction Expansion of e
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