# Is there a closed form solution to this summation?

I'm trying to calculate the expectation of a random variable and I've ended up with the following summation that I need to evaluate. I've tried a number of things including summation by parts, etc, but I can't find a way of solving it. Is there a closed form solution?

$$\sum_{k=0}^{n} \binom nk\frac {p^k (1-p)^{n-k}}{a+k}$$

Here, $a>0$ is an arbitrary integer parameter.

Thanks.

• it leads to a hypergeometric function – Dr. Sonnhard Graubner Dec 15 '16 at 14:37
• @Dr.SonnhardGraubner How would I go about determining the parameters of the hypergeometric function that represents it? – N. Price Dec 15 '16 at 15:52