Find the moment generating funtion of Yn = Xn/n, where Xn has a gamma distribution with parameters alpha = n, and beta.

I'm stuck here. I know that the MGF of a gamma (in this case) is .

The question I have is what to do with the 1/n. I'm pretty sure it works out to be , but I'm not sure why.

Would someone be able to explain this to me?

Thanks in advance.