So I need to find: $\mathbb{E}(\frac{1}{1+N})$ where N is a binomial random variable with paramaters n,p.
I know that when $ Y = g(N)$ $\mathbb{E}(Y) = \sum_{\infty} g(x)p(x)$
where p(x) is the frequency function of N.
So am I on the right track when I right $\mathbb{E}(\frac{1}{1+N}) = \sum_{k=0}^n (\frac{1}{1+k}){n \choose k}p^k(1-p)^{n-k}$
If so how do I proceed from here?
Thanks for any help.