We have recently introduced a quasi-linear (QL) approximation for the solution of the three-dimensional (3-D) electromagnetic modeling problem. In this paper we discuss an approach to improving its accuracy by considering the QL approximations of the higher-order. This approach can be considered the natural generalization of the Born series. We use the modified Green's operator with the norm less than 1 to ensure the convergence of the higher orders QL approximations to the true solution. This new approach produces the converged QL series, which makes it possible to estimate the accuracy of the original QL approximation without direct comparison with the rigorous full integral equation solution. It also opens principally new possibilities for fast and accurate 3-D EM modeling and inversion.