等差级数与等比级数乘积项级数的判敛与求和浅析

Convergence and Summation of Arithmetical Series and Geometric Series Product Series

在级数理论中,一般来说,判断级数的敛散性是比较困难的,有时尽管能判断其收敛,但要求其和却是十分困难的。文中根据等差级数和等比级数的特点,给出了一类基于等差级数和等比级数乘积项的无穷级数的判敛与求和方法。

In series theory, generally, it is difficult to determine the convergence and divergence of se- ries. Though sometimes the convergence can be determined, it is very difficult to determine the summa- tion. Based on the characteristics of the arithmetical and geometric series, a method of summation and con- vergence is put forward, based on arithmetical series and assessment of product of the geometric series of infinite series.