Let $\displaystyle X$~$\displaystyle NB(r,p)$ when $\displaystyle r>=2$ , $\displaystyle p>0$ .

Calculate: $\displaystyle E[\frac{1}{X-1}]$.

I've tried to get any kind of result by calculating the needed sum but got stuck in the middle...I think there's a better way to do it

Hope you'll be able to help me

Thanks in advance