For a given $X_n$ sequence of random variables such that for every $n$, $X_n\sim\mathsf{Geo}\left(\frac{1}{9n}\right)$. I am asked to find $c$ such that $$\mathbb{P}\left[ \lim_{n \to \infty}\frac{X_n}{n} = c \right] = 1$$
So my idea is to use the large number law by that I will define an $X_k'$ for $k =1,2,...,n$ such that $$\sum_{k=1}^{k=n}X_k' \sim\mathsf{Geo}\left(\frac{1}{9n}\right)$$ but how do I find such $X_k'$?