# Cumulative Distribution Function Proof

So I have this proof formula for the Cumulative Distribution Function and I understand it up till the point where we see square brackets, how did those end up there and how did division ended up there????

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It's simply an application of the formula $$\sum_{j=0}^{n-1}r^j=\frac{1-r^n}{1-r}$$ for $r\neq 1$ and $n\geqslant 1$ an integer.
Indeed, $(1-r)\sum\limits_{j=0}^{n-1}r^j=\sum\limits_{j=0}^{n-1}r^j-r^{j+1}$ is a telescopic sum.
See edit. ${}{}$ –  Davide Giraudo Jan 18 '14 at 22:07