TITLE: Method of Proof (Computer Science)
QUESTION [1 upvotes]: Prove that $1+r+r^{2}+...+r^{n-1}=\frac{r^{n}-1}{r-1}$, $r$ a positive integer, $r \neq 1$

REPLY [0 votes]: $\dfrac{r^n - 1}{r-1} = \dfrac{r^n - r^{n-1}}{r-1} + \dfrac{r^{n-1} - r^{n-2}}{r-1} + ...+ \dfrac{r - 1}{r-1} = r^{n-1} + r^{n-2} + ... + 1$
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