数列极限的变式及其教学应用  

The Variant of Limit of Series and Its Application in Teaching

作　　者：易华[1] 熊路红 彩春丽 YI Hua;XIONG Lu-hong;CAI Chun-li(School of Mathematics and Science,Jinggangshan University,Ji’an Jiangxi 343009,China)

机构地区：[1]井冈山大学数理学院,江西吉安343009

出　　处：《萍乡学院学报》2020年第6期12-15,共4页Journal of Pingxiang University

基　　金：井冈山大学信息与计算科学专业建设(2013071029);井冈山大学校级线下一流本科课程“高等数学A2”;教育部高教司产学合作协同育人项目(教育部高教司)(20191230002)。

摘　　要：由于数列极限是函数极限、无穷级数等各种类型极限的基础。因此,其他类型极限变式的等价性推导可以转化为数列极限变式的推导。首先证明了ε-N语言的四个等价命题,然后得到了数列极限定义、数列柯西收敛准则、无穷级数柯西收敛准则、数列收敛到无穷大的变式。最后给出了这些变式命题在教学中的应用。Since limit of series is the basis of limit of function,infinite series and other types of limit,the equivalence derivation of other limit’s variant can be transformed into the derivation of series limit’s variation In this paper,four equivalent propositions of ε-N language are proved,and then the definition of limit of series,Cauchy convergence criterion of series and Cauchy convergence criterion of infinite series are generalized.Finally,the applications of these propositions in teaching are recommended.

关 键 词：数列极限 柯西收敛准则 无穷级数 变式 

分 类 号：O123[理学—数学]