Solving x + x^2 + x^3 +...+ x^n = 1 for any n

michaelkane · Apr 9, 2006

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 · Apr 9, 2006

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

Solving x + x^2 + x^3 +...+ x^n = 1 for any n

Discussion

Similar threads

Undergrad Solving the Difficult Integral ##\int_0^{\infty} x^{n+1} e^{-x} \sin(ax) dx##

Undergrad How Do You Integrate 1/√(x^3 + x^2 + x + 1) dx?

Undergrad Solving x+x^2+x^3+x^4... = 14 for x

High School Why Can't We Cancel (x-2) in the Inequality 2(x+3)(x-2)/(x-2)≥0?

Undergrad How do you solve the definite integral ∫|x^3-x|dx with limits from -1 to 2?

Can I use recursion/induction to show that N <= x < N+1 for x real

Solve Int Partial Fractions: $\int\frac{6{x}^{2}+22x-23} {(2x-1)(x+3)(x-2)} dx$

Undergrad Why Does Integrating x*[x^2(1-x^3)^(n-1)] Result in [(1-x^3)^n] / -3n?

How many real solutions to 2^x = 1+x^2 and 3^x+4^x+5^x = x^2?

High School How Can You Factorize the Polynomial (x+1)(x+2)(x+3)(x+6)-3x^2?