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How can I get the result of this sum:

$$ x + x^2 +...+ x^n $$

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closed as off-topic by graydad, Claude Leibovici, Stefan Hamcke, Sujaan Kunalan, Najib Idrissi Feb 25 '15 at 18:03

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  • $\begingroup$ why did you change the question? $\endgroup$ – Omnomnomnom Feb 25 '15 at 17:43
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Hint: for any $x \in \Bbb R$ with $x \neq 1$, $$ 1 + x + x^2 + \cdots + x^{n} = \frac{1-x^{n+1}}{1-x} $$

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  • $\begingroup$ I am not sure the result makes sense for $x=1$. The right side is not defined while the left side is $n$. The right side should be extended as a limit for $x=1$. $\endgroup$ – Alexander Vigodner Feb 25 '15 at 17:32
  • $\begingroup$ @AlexanderVigodner fixed. We could also have multiplied both sides by the denominator. $\endgroup$ – Omnomnomnom Feb 25 '15 at 17:40
  • $\begingroup$ @AlexanderVigodner: The left side is $n-1$ ;-) $\endgroup$ – Stefan Hamcke Feb 25 '15 at 17:55
  • $\begingroup$ @Stefan Hamcke Well, $n+1$ to be precise :). $\endgroup$ – Alexander Vigodner Feb 25 '15 at 19:26

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