Let $k,l,n\in\mathbb{N}$ with $k+1\leq n$. Find a general formula for $\displaystyle\sum_{i=0}^l \dfrac{l\choose i}{n\choose {k+i}}$.
I think the formula should involve a fraction and a combination. I tried plugging in values of $i$ but I couldn't get anywhere. Next I tried expanding the combinations, but I got a really nasty expression, so that didn't get me anywhere either. Any hints, preferably major, would be nice.