正项级数敛散性的一个新判别法  

A New Criterion for the Convergence of Series with Positive Terms

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：《四川师范大学学报（自然科学版）》2005年第6期667-670,共4页Journal of Sichuan Normal University（Natural Science）

摘　　要：正项级数理论中的Gauss判别法比Raabe判别法更为精细,但又更加复杂,为此给出了正项级数敛散性的一个新判别法,它也是以级数∑∞n=21n(lnn)p为比较标准的,但比Gauss判别法简单.另外,还对新判别法与Gauss判别法的强弱关系进行了讨论.The Gauss Criterion for the convergence of serieses with positive terms is more precise that the Raabe Criterion and, of course, move complicated than the latter. In this paper a new criterion for the convergence of serieses with positive terms is given which is also established based on the comparison with the series ^∞∑n=2 1/n（lnn）^p.The relationship between the Gauss Criterion and the new one is discussed and it is found that new Criterion is somwhat simpler than old one.

关 键 词：正项级数 收敛 发散 判别法 

分 类 号：O174.1[理学—数学]