# Get Mathematica to Apply Chu-Vandermonde Convolution

I'd like to get Mathematica (11) to do basic sums, such as

Sum[Binomial[a, b - k] Binomial[c, d + k], {k, -d, b}].


This is the Chu-Vandermonde sum, which equals ${a+c\choose b+d}$, at least for integer $a,c$.

Mathematica instead evaluates the sum to

Binomial[a, b + d] Hypergeometric2F1[-c, -b - d, 1 + a - b - d, 1],


which is true, but not as useful.

My guess was, that I needed to somehow specify that $a,b,c,d$ were positive integers, or something, so I entered the following (BTW, is there an easier way to do this?)