Let X∼Binomial(n,p)X \sim \text{Binomial}(n, p)X∼Binomial(n,p). Find E[1/(X+1)]E[1/(X+1)]E[1/(X+1)].
1−(1−p)n+1(n+1)p\frac{1-(1-p)^{n+1}}{(n+1)p}(n+1)p1−(1−p)n+1
1np+1\frac{1}{np+1}np+11
pn+1\frac{p}{n+1}n+1p
1−pn+1\frac{1-p}{n+1}n+11−p