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Math Help - Consider the following equation

  1. #1
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    Consider the following equation

    Consider the following eq. Find value of x. Also, is this equation: Trancendental, Gauss Seidel, Newton-Raphson or Algebraic?

    x=1/(x-1/(x+1/(x-1/(x+1/(x-1/(x+1/(x-1/(x+1/(x-1/(x+1/(x-1/(x+1.......infinity

    here's a better look at what it looks like....

    x=1/(x-1/(x+1/(x-1/(x+1/(x-1/(x+1/(x-1/(x+1/(x-1/(x+1/(x-1/(x+1 - Wolfram|Alpha

    Any input would be really awesome.
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  2. #2
    Behold, the power of SARDINES!
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    Re: Consider the following equation

    Quote Originally Posted by anol1258 View Post
    Consider the following eq. Find value of x. Also, is this equation: Trancendental, Gauss Seidel, Newton-Raphson or Algebraic?

    x=1/(x-1/(x+1/(x-1/(x+1/(x-1/(x+1/(x-1/(x+1/(x-1/(x+1/(x-1/(x+1.......infinity

    here's a better look at what it looks like....

    x=1/(x-1/(x+1/(x-1/(x+1/(x-1/(x+1/(x-1/(x+1/(x-1/(x+1/(x-1/(x+1 - Wolfram|Alpha

    Any input would be really awesome.

    If you assume that it converges then the pattern repeats its self and you get the equation

    x=\frac{1}{x-\frac{1}{x+ ...}}


    the ... is just x nested inside itself. This gives

    x=\frac{1}{x-\frac{1}{x+ x}} \iff x=\frac{1}{\frac{2x^2-1}{2x}} \iff x=\frac{2x}{2x^2-1} \iff 2x^2-1=2

    Just finish solving for x.

    As for the name I have no idea other than it is a continued fraction.
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  3. #3
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    Re: Consider the following equation

    You're the man.
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  4. #4
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    Re: Consider the following equation

    It's transcendental btw because if you plot y=x and y=(2x)/(2x^2-1) the intersection points are at 1.224 which is the value of x.
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