How can I get the result of this sum:
$$ x + x^2 +...+ x^n $$
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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Hint: for any $x \in \Bbb R$ with $x \neq 1$, $$ 1 + x + x^2 + \cdots + x^{n} = \frac{1-x^{n+1}}{1-x} $$