The question I'm looking at involves evaluating:
$$ E[\frac{(n-1)}{(n-1+X_n)}] $$ for n >= 2
Xn is a random variable with a negative binomial distribution, equivalent to Binomial(p, -n).
How would I go about evaluating this expectation? I've never dealt with taking the expectation of a function which used the parameter of the number of trials and don't know where to start.
I know that the solution is 1-p, but I do not know how to get there.