Let X∼Binomial(n,p)X \sim \text{Binomial}(n, p)X∼Binomial(n,p) where n≥1n \ge 1n≥1 and 0<p<10 < p < 10<p<1. What is the expected value of the random variable 1X+1\frac{1}{X+1}X+11?
1−(1−p)n+1(n+1)p\frac{1 - (1-p)^{n+1}}{(n+1)p}(n+1)p1−(1−p)n+1
1(n+1)p\frac{1}{(n+1)p}(n+1)p1
(1−p)n+1(n+1)p\frac{(1-p)^{n+1}}{(n+1)p}(n+1)p(1−p)n+1
1np\frac{1}{np}np1