This paper presents Dirichlet series and approximate analytical solutions of magnetohydrodynamic (MHD) flow due to a suction / blowing caused by boundary layer of an incompressible viscous flow. The governing nonlinear partial differential equations of momentum equations are reduced into a set of nonlinear ordinary differential equations (ODE) by using a classical similarity transformation along with appropriate boundary conditions. Both nonlinearity and infinite interval demand novel mathematical tools for their analysis. We use elegant fast converging Dirichlet series and approximate analytical solutions (method of stretching of variables) of these nonlinear differential equations. These methods have advantages over pure numerical methods for obtaining derived quantities accurately for various values of the parameters involved at a stretch and also they are valid in much larger parameter domains as compared with DTM-Padé and classical numerical schemes.