p-级数散敛性的2种简易证明方法  

Two simple proof methods of the convergence and divergence for the p-series

作　　者：王里青 王长有 WANG Li-qing;WANG Chang-you(School of Applied Mathematics,Chengdu University of Information Technology,Chengdu 610225,China)

机构地区：[1]成都信息工程大学应用数学学院

出　　处：《高师理科学刊》2019年第11期6-8,共3页Journal of Science of Teachers＇College and University

基　　金：四川省应用基础研究项目(2018JY0480)

摘　　要：p-级数是数项级数中一类特别重要的正项级数,通常被作为比较级数,结合级数散敛性的比较判别法及比较判别法的极限形式来证明其它正项级数的散敛性.关于p-级数散敛性的证明已有很多种方法,如比值审敛法、定积分证明法、柯西审敛法、比较审敛法和级数收敛定义法等.利用李海涛教授1984年证明的关于正项级数散敛性判定的一个公式,给出证明p-级数散敛性的2种简易证明方法.通过这些证明,能激发学生对级数的学习和研究的兴趣,该方法也可用来证明其它级数的散敛性.The p-series is one of the most important positive series,it is usually used as a comparison series to prove the divergence and convergence of other positive series by combining comparison discriminant method or the limit form of comparison discriminant method.There are many methods to prove the divergence and convergence of p-series,such as ratio convergence method,definite integral proof method,Cauchy′s convergence method,comparison convergence method,series convergence definition method and so on.Two simple methods are given to prove the divergence and convergence of p-series by using a formula proved by professor LI Hai-tao in 1984.Through these proofs,students′interest in series learning and research can be stimulated,and this method can also be used to prove the divergence and convergence of other series.

关 键 词：P-级数 收敛 发散 

分 类 号：O173[理学—数学]