Find x: A Simple Formula to Solve x + x^2 + x^3 +...+ x^n = 1

[michaelkane]

I need to calculate easy solution for following equation.

x + x^2 + x^3 +...+ x^n = 1

I need a simple formula to calculate value of x that satisfies above equation for any value of n.

This is for accounting/MBA has nothing to do with Physics, but I am sure anyone will be able to help me out.

Thanks.

 

[arildno]

Using the geometric series identity: x+x^{2}+...+x^{n}=x\frac{x^{n}-1}{x-1}
we may reformulate your equation to:
x^{n+1}-2x+1=0
I'm not too sure there exist a nice, general solution of this for arbitrary n.