MHB Why Does This Summation Simplify to a Power of p?

[pp123123]

I came across some summation but have no idea how to simplify it.

$\sum_{x=0}^{\infty} \binom{x+r-2}{r-2}(1-p)^{x}=p^{1-r}$

Why is it so?

 

[Opalg]

I came across some summation but have no idea how to simplify it.

$\sum_{x=0}^{\infty} \binom{x+r-2}{r-2}(1-p)^{x}=p^{1-r}$

Why is it so?

Hint: Use the binomial series $$(1+x)^\alpha = \sum_{k=0}^\infty {\alpha\choose k}x^k,$$ with $x = -(1-p)$ and $\alpha = 1-r.$