Result R4805: Dual probability distribution function for geometric random positive integer shows that \begin{equation} \mathbb{P}(N > n) = (1 - \theta)^n \end{equation} Thus \begin{equation} \mathbb{P}(N \leq n) = 1 - \mathbb{P}(N > n) = 1 - (1 - \theta)^n \end{equation} $\square$