Hitting a Fixed Target with a Growing Die

, 2, \ldots, n$) infinitely many times and keep a running total of all the rolls. Let $f(n,k)$ be the probability that this running total is ever exactly equal to $k$, for a fixed integer $k \geq 1$. For a fixed value of $k$, compute $\lim_{n \to \infty} f(n,k).$ Report your answer for $k = 6$.