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How can I isolate $x$ in terms of $n$, considering the following restriction?

$$1 = x + x^2 + x^3 + x^4 + … + x^n$$

For example $f(n=3) = 0.544$

Other hints:

  • Only positive values of $x$ are accepted
  • Approximated results are also valid
Evandro
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    @b00nheT: this is in fact of no use. –  Oct 21 '18 at 16:08
  • Hi @b00nheT, can you please explain your point? My target here is to create a function that receives a $n$ parameter and return $x$. – Evandro Oct 21 '18 at 16:22

1 Answers1

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Polynomial equations of this type have no closed-form expression for $n>4$.

  • well, this can be also expressed as a ∑, and it is really close to the geometric series sum. Knowing this, there are no methods to simplify it? – Evandro Oct 21 '18 at 16:06
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    @EvandroMuchinski: sorry, no. Being "really close to" is not enough. –  Oct 21 '18 at 16:07