If $\tau \equiv \min\{n:X_1+ X_2 +\cdots+ X_n > k\}$, how to show $\mathbb{E}(\tau) = 1 + {k \over \mu}$ for exponential random variables?

Question

Let $X_1, X_2, \ldots$ be i.i.d where $X_i \sim \mathrm{Exponential}(\frac{1}{\mu})$, and suppose $k$ is a positive constant. Define $\tau \equiv \min\{n:X_1+ X_2 +\cdots+ X_n > k\}.$ I would like to show that $\mathbb{E}(\tau) = 1 + {k \over \mu}.$ Is there a way to use Wald's theorem for this?