The method of evaluating the electrostatic energies in partially periodic systems, proposed by J. Lekner [Physica A 157, 826 (1989)] and extensively developed by Gronbech-Jensen and co-workers [N. Gronbech-Jensen, Int. J. Mod. Phys. C 8, 1287 (1997) and N. Gronbech-Jensen, G. Hummer, and K. M. Beardmore, Mol. Phys. 92, 941 (1997)] is examined in the context of numerical simulations. The main practical problem in its applications is described analytically and illustrated on very simple numerical computations on a system of two charged hard spheres. The main results are a study of the convergence of these summations for the simple system of two charged hard spheres and to warn against possible systematic bias in numerical simulations (Monte Carlo and molecular dynamics) that may be induced by straightforward applications of this method.