1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    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).
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Continued Fractions - Exact Solution
  1. Continued Fractions. (Replies: 1)

  2. Continued Fractions (Replies: 4)