Question

I have this change of indexes in a double sum:\[\sum_{j=0}^{\infty} \sum_{k=0}^{\infty} \frac{z^j}{j!} \frac{w^k}{k!} = \sum_{n=0}^{\infty} \sum_{k=0}^{n} \frac{z^{n-k}}{(n-k)!} \frac{w^k}{k!}\]. How do we change the summation indexes here? I'm not too clear on how to get k=0 to n for the inner sum.