2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68025We give an Euler Maclaurin formula with remainder for the sum of the values of a smooth function on the integral points in a simple integral polytope. This formula is proved by elementary methods.25 pages. Also see our previous paper in Proc. Nat. Acad. Sci. 100 no. 2 (2003), 426-433. Revision: added Euler Maclaurin formulas for symbols and for polynomialsCombinatoricsSymplectic Geometry65B15; 52B20text