Renewal Theory Convergence

Question

Let $X_1, X_2, X_3,...$, with mean $\mu = E(x) \in (-\infty,\infty]$. Let $T_; = X_1+X_2+...+X_k$ for $k=1,2,...$ is the time of the k-th renewal with $T_0=0$. Let $N_n = max{k: T_k \leq n}$ for $n=1,2,...$ is the number of renewals in $(0,n]$.

Then, 1) Using the WLLN, for the case $\mu < \infty$, prove $\frac{u_1+...+u_n}{n} \rightarrow \frac{1}{u}$.

2. Do the same but for the case $\mu = \infty$

3. Prove $\mu=\infty$ case of the SLLN from the finite mean case.

There are a couple question before these which I can solve, but I am struggling with these. Any hints?

Thank you.