正项级数敛散性的两个判别法

Two Criteria for Convergence or Divergence ofthe Positive Term Seriers

没有一个正项级数是收敛得“最慢的”,也没有一个正项级数是发散得“最快的”,也就是不存在一个正项级数,用它可以作为判定其它所有正项级数敛散性的标准.我们只能从一些巳知级数的敛散性逐步建立一些判别法.从理论上讲这条愈来愈精细的判别法的链条是可以无限制地继续下去的.该文建立两个判别法,为这个链条添上两环.

:There is not a positive term series which converges most slowly,and neither is there a positiveterm series which diveges most quickly. That is to say,no one positive term series can be a criterion to deter-m..ne the convergence or divergence of all positive term series. We can only establish some criteria from con-vergences or divergences series known. In theory one might say that the more exact and more sharp chain ofcriteria can be continued indefinitely. In this paper,we establish two criteria to determine the convergence or divergence of some positive term series.