Suppose an unbiased coin is flipped independently infinitely many times. Let $T_n$ be the minimum number of flips to get $n$ heads. Show that $T_n/n \rightarrow c$ a.s. and compute $c$.
My approach: Let X_i(\omega) be the random variable such that, $X_i(\omega) = 1$ if the $i-th$ toss is heads and $0$ otherwise.
$P(X_i(\omega) = 1) = 1/2$ and $P(X_i(\omega) = 0) = 1/2$, for all $i = 1,2,3,...$
$T_n(\omega) = \inf_{M \geq n }\{M:\sum_{i = 1}^{M} X_i(\omega) = n$}.
How do I proceed from here on? I think the Strong Law of Large numbers needs to be used as I need to prove almost sure convergence.