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Quick solution

  1. Apr 9, 2006 #1
    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.
     
  2. jcsd
  3. Apr 9, 2006 #2

    arildno

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    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.
     
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