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The geometric distribution is:
Pr(X=k) = (1-p)k-1p for k = 1, 2 , 3 ...
A geometric series is a+ ar+ ar2, ... or ar+ ar2, ...
Now the sum of all probability values of k = Pr(X=1) + Pr(X = 2) + Pr(X = 3) ...
= p + p2+p3 ... is a geometric series with a = 1 and the value 1 subtracted from the series.
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