# Can you please help me find the Moment generating function of the negative binomial when it looks a bit different?

f(x) = $\binom{(r+x)-1}{x-1}p^{r}(1-p)^{x}$ noting 0 < p<1 and r>0 $$\sum_{X}^\infty \binom{(r+x)-1}{r-1}p^{r}(1-p)^{x} =1.$$ x=0,1,2,3......... I think it looks like this: $$\sum_{X}^\infty \binom{(r+x)-1}{r-1}p^{r}(1-p)^{x} =$$ I think i put an e^tx inside of the sumation. But do i try to turn all the x's to x+r or the r's to r+x?

-

$${x+r-1 \choose x-1}={x+r-1 \choose r}$$