Kummer判别法的改进和推论

On kummer Method and Its Relevant Corollaries

对于正项级数,判定其敛散性有许多方法,常用的有达朗贝尔判别法,柯西判别法等,但有些级数用此二法不能判定其敛散性,比如在此二法中极限为1的正项级数.在这篇文章中,将给出判定正项级数敛散性的另外一种方法以及一些相关的推论,解决了以上的问题.

For positive series ,there are many methods of judging its convergence and divergence.Usually we can use the methods such as D Alembert and Cauchy . But it is impossible to determine the convergence and divergence for some series with them,such as some positive series whose limit is equal to one.In this paper ,we introduce another method of judging convergence and divergence of positive series and some relevant corollaries to solve these problems .