I am trying to find a closed form for the following summation, where $a<n$, and $n$ is a fixed constant: $$\sum_{r=1}^a\frac{1}{r(n-r)}$$ Do you have any ideas about how I'd go about doing this? Formulae for specific values of $n$, as well as any hints, would also be very helpful. Unfortunately I can't show any working or my attempts as I simply don't have any idea about how I'd proceed.
Thank you for your help.