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Math Help - Value of a continued fraction.

  1. #1
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    Value of a continued fraction.

    THe following is called a continued fraction. It equal an irrational number. Find that number.
    It is basically
    2 plus half+ half of half + half of half of half.....
    It just keep on going
    i really need your help
    Last edited by mr fantastic; May 15th 2010 at 04:16 PM. Reason: Re-titled.
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  2. #2
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    Quote Originally Posted by vvc531 View Post
    THe following is called a continued fraction. It equal an irrational number. Find that number.
    It is basically
    2 plus half+ half of half + half of half of half.....
    It just keep on going
    i really need your help
    U(n) = 2+(\frac{1}{2})^n

    We can treat the right hand side as a geometric sequence:

    a = \frac{1}{2} , r = \frac{1}{2} n = infinity

    S(infinity) = \frac{a}{1-r} = \frac{0.5}{1-0.5} = 1

    this means the sum of the infinite terms is 1 and adding this to the existing 2 we get a limit of 3
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