正项级数收敛性的又一新判别法  

Another new judge method of convergence of positive series

作　　者：杨钟玄[1] 

机构地区：[1]天水师范学院数学系,甘肃天水741001

出　　处：《贵州师范大学学报（自然科学版）》2005年第4期73-76,共4页Journal of Guizhou Normal University：Natural Sciences

摘　　要：近年来,关于正项级数收敛性判别法又有一些新的研究,其中主要是得到了一些关于收敛性的新判别法以及对有关判别法的强弱进行了讨论.本文建立了正项级数收敛性的又一个新判别法,它适用判别与级数∑∞n=21n(lnn)s敛散速度相当的正项级数的敛散性,因而新判别法比传统的Raabe判别法等更为精细.此外,通过与Gauss判别法进行比较,得出了新判别法强于Gauss判别法的结论.In recent years, some new researches have been arisen on the judge method of convergence of positive series. The main results are some new judge methods of convergence and some relations of strength of the judge methods concerned were obtained. In this paper we have founded another new judge method of convergence of positive series. This method is applied to the judge of convergence of series, the convergence velocity of which is equal to the series ∑∞n=2（1）/（n（lnn）^s）. So the new judge method is more careful than the Raabe method. Moreover, through comparison between the new method and Gauss method, we have obtaind the conclusion that the new judge method is stronger than Gauss method.

关 键 词：正项级数 收敛 发散 判别法 

分 类 号：O174.1[理学—数学]