g(x; p) = p(1 − p)^(x-1), x = 1, 2, . . .
0, else
How can I find an expression for the cumulative probability distribution for this variable? That is, F(x) = P(X (less or equal to x)
Is this what you are asking $\displaystyle \sum\limits_{x = 1}^n {p\left( {1 - p} \right)^{x - 1} } = 1 - \left( {1 - p} \right)^n ~?$