调和级数发散性的多种证明方法.doc

邯郸学院本科毕业论文
高昌
摘要调和级数是数学分析中一个典型的正项发散级数,,,笔者把这些方法分别归在了比较类、柯西类、,笔者在对各种方法进行整理时,对原来有些方法的书写和步骤都有所改动,呈现形式与原证不同.
关键词调和级数发散性判别收敛
Proofs of the divergency of harmonic series
Gao chang Directed by Associate Prof. Lou Xijuan
Abstract Harmonic series is the mathematical analysis of a typical positive divergent series, proof it divergent method has a lot of. This article mainly gives proof harmonic diverges 11 kinds mon methods. The author will gather to proof method of harmonic diverges underwent further consolidation, make it e a set of has a simple logical system. According to the characteristics of various methods, the author put these methods pared respectively in classes, cauchy class, integral classes and series and four categories such as infinite. In each categories below two to four different methods of proof. In order to facilitate parison of various methods, the author put together in various methods to the original collation, some methods of writing and steps are varies, present form and the original
license different.
Key words Harmonics Series Divergency Discriminate Convergency

目录
摘要 I
外文页 II
1 引言 1
2 调和级数发散性的证明方法 1
比较类 1
柯西类 3
积分类 4
和为无穷大类 5
3 总结 7
参考文献 8
致谢 9
调和级数发散性的多种证明方法
1 引言
调和级数是级数中具有代表性的一个级数,,,,,按照比较、柯西、积分、和为无穷大四个条件进行简单归类,使之形成一套比较完备的体系,,《数学分析》中级数敛散性学习和研究,尤其是初学者,会有很大帮助.
2 调和级数发散性的证明方法
比较类
,利用我们所熟知的收敛或发散的级数与未知的级数进行比较,就能得出结论.
对于调和级数,,把原级数变形,,并且它的通项与调和级数的通项比是一个非零常数,,后两种是第二种思路.
方法1
依次将一项,一项,二项,四