Abstract: This article takes a type of recursive sequence xn + 1 = f (xn )，n = 0,1,2,⋯, determined by a function y = f（x）as the research object. Assuming that f（x）is monotonic, and in the absence of a general term formula, the method for judging the convergence and divergence of the sequence of {xn} is proposed, and the general law of the judgment method is summarized. Finally, specific applications are given to verify the effectiveness and feasibility of the method.