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.