# Consider the following equation

• Feb 24th 2013, 04:18 PM
anol1258
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.
• Feb 24th 2013, 05:15 PM
TheEmptySet
Re: Consider the following equation
Quote:

Originally Posted by anol1258
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

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

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

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

Just finish solving for x.

As for the name I have no idea other than it is a continued fraction.
• Feb 24th 2013, 05:23 PM
anol1258
Re: Consider the following equation
You're the man.
• Feb 24th 2013, 05:25 PM
anol1258
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.