Finding expected value for negative binomial distribution

Question

Let $X\in NB(p,r)$, I need to find the expected value of $1/(X-1)$. Can I use the fact that $E[X]$=$r/p$ when solving or am I on the wrong track?

Answer 1

Hint Let $h(x) = \frac{1}{X-1}$ then find $E[h(x)] = \sum_{x=r}^\infty h(x) × P(X=x) $ where $P$ is the pdf of the negative binomial