Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Continued Fractions - Exact Solution

  1. Nov 26, 2007 #1
    I'm dealing with the fraction:
    1+1
    1+1/(1+1)
    1+1/(1+1/(1+1))
    ...

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

    (k+or-sqar(k^2+4))/2

    Which here is
    (1+or-sqar(5))/2

    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

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    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).
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook