IS AN EFFECTIVE LAGRANGIAN A CONVERGENT SERIES

We present some generic arguments demonstrating that an effective Lagr angian L(eff) which, by definition, contains operators O-n of arbitrar y dimensionality in general is not convergent, but rather an asymptoti c series. It means that the behavior of the far distant terms has a sp ecific factorial dependence L(eff) similar to Sigma(n)(c(n)O(n)/M(n)), c(n) similar to n!, n much greater than 1. We explain the main ideas by using QED as a toy model, However we expect that the obtained resul ts have a much more general origin. We speculate on possible applicati ons of these results to various physical problems with typical energie s from: 1 GeV to the Planck scale.