The design of safe grounding systems in electrical installations is essential to assure the protection of the equipment, the power supply continuity and the security of the persons. In order to achieve these goals, it is necessary to compute the equivalent electrical resistance of the system and the potential distribution on the earth surface when a fault condition occurs. In the last years the authors have developed a numerical formulation based on the BEM for the analysis of grounding systems embedded in uniform and layered soils. As it is known, in practical cases the underlying series have a poor rate of convergence and the use of multilayer soils requires an out of range computational cost. In this paper we present an efficient technique based on the Aitken δ2-process in order to improve the rate of convergence of the involved series expansions.