How to calculate the sum $x + x^2 +…+ x^n$ [closed]

How can I get the result of this sum:

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

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

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• why did you change the question? – Omnomnomnom Feb 25 '15 at 17:43

Hint: for any $x \in \Bbb R$ with $x \neq 1$, $$1 + x + x^2 + \cdots + x^{n} = \frac{1-x^{n+1}}{1-x}$$
• 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 $x=1$. – Alexander Vigodner Feb 25 '15 at 17:32
• @AlexanderVigodner: The left side is $n-1$ ;-) – Stefan Hamcke Feb 25 '15 at 17:55
• @Stefan Hamcke Well, $n+1$ to be precise :). – Alexander Vigodner Feb 25 '15 at 19:26