数学毕业论文 级数敛散性的判别方法.doc

淮北师范大学信息学院 2012 届学士学位论文 级数敛散性的判别方法 系 别: 数学系 专 业: 数学与应用数学 学 号: 20081884083 姓 名: 赵 高 指 导 教 师: 陈冬君 指导教师职称: 讲 师 2012年 5 月 10 日 级数敛散性的判别方法 赵 高 (淮北师范大学信息学院，淮北，235000) 摘 要 级数有很多重要的性质，其中敛散性是级数的一个非常重要的性质，敛散性的判别方法也一直是人们研究的热点.通过判别级数的敛散性进一步了解级数的性质.本文探论了正项级数、交错级数以及任意项级数敛散性的判别方法，正项级数通项的多变性,决定了判别正项级数敛散性的方法会有多种当然由于通项的特殊性也会有特殊的方法判别.本文通过归纳一些判别正项级数敛散性的方法,The Convergence of the Series of Discriminant Method Zhao Gao College of Information Technology Huaibei Normal University, Huaibei,235000 Abstract The series has a lot of important properties, which is the series convergence and divergence of a very important properties, criteria for convergence and divergence has been the focus of study. Through judging the convergence of series to further understand the series nature. This article of the series of positive terms, staggered series as well as any series convergence and divergence sexual discriminant method, a series of positive terms, staggered series, series of any general variability, determines the identification of series of positive terms, staggered series, any of the convergence of the series will have a variety of methods, mainly the dAlembert discriminant method, Cauchy method, Leibniz method, di Like dilichlet discriminance. Of course due to the particularity of the general will also have the special methods of discriminant. This paper summarized some criteria for positive term series and the convergence of alternate series method, let people in the learning process of convergence of series of discriminant can be a very good grasp of, and grasp the discriminant conditions. Key words: Series of positive terms，Alternating series，Convergence and divergence，Discriminant analysis method 目录 引言 1 一、级数及其敛散性的有关概念 1 二、正项级数敛散性的判别方法 2 1、比式判别法（达朗贝尔判别法） 2 2、根式判别法（柯西判别法） 3 3、拉贝判别法 4 4、高斯判别法 5 5、对数判别法