Energy of the electron gas perturbed by a constant electric field is examined to the eighth order of the Rayleigh–Schrödinger perturbation series. The method of the calculation is based on the local density approach to the non–interacting many–electron system in which the electron wavefunctions are represented by the standing–like waves. The convergence of the series depends on the strength of the electric field, the radius of the metal sample and the quantum number defining the electron energy. For the case of convergence a decisive contribution to the perturbation energy is obtained from the second–order term. This term gives the electric polarizability to be only slightly different from that obtained in the former theories. For the sake of comparison the high–order perturbation calculation done for a three–dimensional electron gas is repeated also for the case of the one– and two–dimensional electron gas systems having a finite size.