2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/32261We present a partial proof of van Hoeij-Abramov conjecture about the algorithmic possibility of computation of finite sums of rational functions. The theoretical results proved in this paper provide an algorithm for computation of a large class of sums $ S(n) = \sum_{k=0}^{n-1}R(k,n)$.LaTeX 2.09, 7 pages, submitted to "Programming & Computer Software"Symbolic ComputationDiscrete MathematicsI.1.2text