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Continued Fractions - Exact Solution

  1. Nov 26, 2007 #1
    I'm dealing with the fraction:

    After viewing another similar forum I found that they came up with the equation


    Which here is

    My question is how did they derive that equation?
    I need to show proof of that equation working using the fraction...
  2. jcsd
  3. Nov 26, 2007 #2


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    Call the result x, that is
    [tex]x = \frac{1}{1 + \frac{1}{1 + \frac{1}{1 + \cdots}}}[/tex]
    Then you recognize x again in the right hand side:
    [tex]x = \frac{1}{1 + x}[/tex]
    Now solve this for x (it's just a quadratic equation).
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