\begin{align*} P(X \le x) & = 1 - P(X \gt x)\\ & = 1- \sum_{k={x+1}}^{\infty} {(1-p)^{k-1}p}\\ & = 1- p \frac{(1-p)^{x}}{1-(1-p)}\\ & = 1- (1-p)^{x} \end{align*}