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Math Help - infinite continued fraction

  1. #1
    Newbie
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    Oct 2011
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    infinite continued fraction

    Hi, I mostly know how to do a question like this if it was finite, but since it is infinite I need some help.

    q: express the continued fraction expansion [1,5,1,5,1,5,...] in the form

    \frac{a+b \sqrt{c}}{d} where a,b,c and d are integers.

    Thanks for any help.
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  2. #2
    MHF Contributor

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    Re: infinite continued fraction

    Let
    x= 1+\frac{5}{1+ \frac{5}{1+ \cdot\cdot\cdot}}
    From which it follows that x= 1+ 5/x.
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