Proof of a Combinatorial Identity

In this paper we prove an interesting identity involving combinatorial symbols. The theorem was discovered while we were studying Calculus in the ”Mathematics 2” course at the USAC/CUNOC University in Quetzaltenango, Guatemala, between 2002 and 2003. The identity arose from some equations involving the relationship between delta and epsilon for polynomials, in some definitions of calculus, and Newton’s binomial theorem. The finished work won a prize in a demonstration contest at a university science fair, to which we were invited, at Rafael Landivar University on June 13, 2003.