Let $G_n \in \text{Geometric}(\theta_n)$ be a D4001: Geometric random positive integer for each $n \in 1, 2, 3, \ldots$ such that
Let $a \in (0, \infty)$ be a D5407: Positive real number.
| (i) | \begin{equation} \forall \, n \in 1, 2, 3, \ldots : \theta_n = \frac{1}{n} \end{equation} |
Then
\begin{equation}
\lim_{n \to \infty} \mathbb{P} \left( \frac{G_n}{n} \leq a \right)
= 1 - e^{-a}
\end{equation}