Can anyone give a reference, a proof, or a reference that explains why Maple can evaluate this identity mathematically correctly:


$$n-i-1=(d-1)\sum\_{l=1}^{n-i-1}\frac{\binom{n-i-1}{l}}{\binom{n-i+d-3}{l}}$$



Rational Binomial Identity
The canonical reference for this sort of thing is Petkovsek and Zeilberger's book "A=B". Maple (almost certainly) uses the Zeilberger-Wilf algorithm for hypergeometric summation (which really goes back to Bill Gosper). You can also read the Wilf-Zeilberger paper (Inventiones, around 1990).


