Given two independent random variables $X_1\in NB(p,r_1)$ and $X_2\in NB(p,r_2)$, find the distribution of random variable $X_1+X_2$
I came up with an answer that is obviously wrong since it's different from what's on the textbook ( $X_1+X_2 \in NB(p,r+s)$), how do I go about showing this?