正项级数比较判别法极限形式的探析  

Exploration and analysis on the limit form of positive series comparative discriminant method

作　　者：于也淳 邓雪[2] YU Ye-chun;DENG Xue(School of Software Engineering,South China University of Technology,Guangzhou 510640,China;School of Mathematics,South China University of Technology,Guangzhou 510640,China)

机构地区：[1]华南理工大学软件学院,广东广州510640 [2]华南理工大学数学学院,广东广州510640

出　　处：《高师理科学刊》2019年第12期6-8,共3页Journal of Science of Teachers＇College and University

基　　金：2018年中国高等教育学会理科教育专业委员会研究课题（Y1181511）;2016年广东省教改项目（Y1172190）;2019年华南理工大学教改项目（Y1190761）;2017年广东省本科高校教学改革工程建设项目——公开在线课

摘　　要：大部分高等数学教材都是从极限义出发,给出正项级数比较判别法极限形式的证明方法.从函数极限义的一个等价条件出发,利用无穷小的思路,给出正项级数比较判别法极限形式新的证明方法,对原来的理进行完善,同时给出具体实例说明该理的几种特殊情况.这些结论对正项级数敛散性的判有一的理论意义.Most of the higher mathematics textbooks give the proof of limit form of positive series comparison discriminant method based on the definition of limit.Starting from an equivalent condition of the definition of function limit and using the idea of infinitesimal,gives a new proof method of limit form of positive series comparison discriminant,perfects the original theorem,and gives some concrete examples to illustrate some special cases of the theorem.These conclusions have certain theoretical significance for the determination of convergence and divergence of positive series.

关 键 词：正项级数 比较判别法 极限 无穷小 

分 类 号：O173[理学—数学]