Suppose that X and Y are independent Poisson random variables with parameters $\displaystyle \lambda$

and μ respectively. Find P(X+Y=n).

My attempt so far:

I use the fact that P(X=k,Y=m)=P(X=k)P(Y=m) because of independence. I then set about finding this probability when k+m=n but my solution still ends up with k's in it. Any thoughts?