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.

Re: Consider the following equation

Quote:

Originally Posted by

**anol1258**

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.

Re: Consider the following equation

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.