So hopefully you're pretty satisfied that this limit is equal to e to the a. And then one other toolkit I want on our belt, and I'll probably actually do the proof in the next video, the other toolkit is to recognize that x factorial, let me do this, x factorial over x minus k factorial is equal to x times x minus 1 times x minus 2, all the way down to times x minus k plus 1. And we've done this a lot of times, but this is the most abstract we've ever written it. I can give you a couple of examples. And they'll be exactly, and just so you know, they'll be exactly k terms here. 1, 2, 3, this is the first term, second term, third term, all the way, and this is the kth term. And this is important to our derivation of the Poisson distribution.