正项级数审敛法探究  

Study on the criterion of judging the convergence and divergence for positive series

作　　者：李卫平[1] 纪宏伟[1] LI Wei-ping;JI Hong-wei(Department of Mathermatics and Physics,Nantong Normal College,Nantong 226010,China)

机构地区：[1]南通师范高等专科学校数理系,江苏南通226010

出　　处：《高师理科学刊》2018年第11期5-8,共4页Journal of Science of Teachers＇College and University

基　　金：江苏省教育厅高校"青蓝工程"(2018)资助项目

摘　　要：借助级数∞∑n=21/1(lnn)~r(r≥1)利用比较原则,推出了判别正项级数敛散性的一个新方法,并在此基础上得到了通项递减的正项级数的一个审敛法.所给结论强于双比值判别法,且利用所得结论判断p-级数∞∑n1/n^p的敛散性比以往判断方法均简单.A new criterion of judging the convergence and divergence for positive series is presented by comparison to(∞∑n=2)1/n(㏑n)^r(r≧1).And on this basis,obtains a theorem about the criterion of judging the convergence and divergence for the general decline positive series.The new conclusions are better than double ratio method,and it is easier to judge the convergence and divergence of(∞∑n=1)1/n^pby using new conclusions than any other method.

关 键 词：正项级数 通项递减的正项级数 敛散性 

分 类 号：O173[理学—数学]