  The standard lattice perturbation theory leads to the asymptotic series
because of the incorrect interchange of the summation and integration. However,
changing the initial approximation of the perturbation theory, one can generate
the convergent series. We study the lattice $\phi^4$-model and compare the
operator $\langle\phi_n^2\rangle$ calculated using the convergent series and
obtained by Monte Carlo simulations.
