## Help with renewal theory

I've a question i can't solve.

1) Consider a M/G/infinity queue where customers arrive according to a Poisson process with rate $\lambda$ and let the service times of the customers be iid r.v. with finite mean $\mu$. Then the limiting distribution is $Po(\lambda \mu)$. Now, let the r.v. L be the length of a busy period. A busy period begins when an arrival finds the system empty and ends when there are no longer any customers in the system. Use the renewal-reward theorem to show that $E[L]=\frac{e^{\lambda \mu}-1}{\lambda}$.