收敛正项级数余项的一个性质及应用  

Property and Application of Remainder in Convergent Positive Series

作　　者：施俊 彭庆英 刘建忠 SHI Jun;PENG Qingying;LIU Jianzhong(School of Mathematics and Physics,Jiangsu University of Technology,Changzhou Jiangsu 213001,China;Fundamentals Department,Changzhou Technician College Jiangsu Province,Changzhou Jiangsu 213018,China)

机构地区：[1]江苏理工学院数理学院,江苏常州213001 [2]江苏省常州技师学院基础部,江苏常州213018

出　　处：《大学数学》2025年第1期95-99,共5页College Mathematics

基　　金：2021年江苏省科技厅自然科学基金面上项目(BK20211358);2023年江苏省高等教育质量保障与评价研究课题(2023-Y06)。

摘　　要：正项级数的余项级数可以判断某些复杂级数的敛散性.利用富比尼定理,通过交换正项级数的次序,给出了收敛正项级数的余项所构成的级数收敛的充要条件,在此基础上定义了任意级数的伴随级数.实例表明所给结果可用于判断一些较复杂级数的敛散性.The series formed by the remainder of the positive series can judge the convergence and divergence of some more complex series.By using the Fubini theorem and by exchanging the order of positive series,the necessary and sufficient conditions for the convergence of the series formed by the remainder of the convergent positive series are given.On this basis,the adjoint series of any series is defined.Examples show that the results can be used to judge the convergence and divergence of some more complex series.

关 键 词：收敛正项级数 余项级数的收敛性 富比尼定理 伴随级数 

分 类 号：O173-4[理学—数学]