In quantum mechanics，the wave function must obey the three standard conditions，such as single value，continuous and finite，which give naturally energy quantization after the wave function under such conditions.The determination of convergence and divergence of infinite series is very important in quantum mechanics. The current textbooks use basically the same grade diverging to show that the series diverges.In comparison with divergent series，we adopt a more easy method to make students understand，find a better rather than the first series of small divergent series，and then prove little diverges，to illustrate that the series of great divergence.This interpretation not only enables students to accept quickly，more important is logically more complete.