调和级数发散性的多种证明方法.doc

I 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, 11 ,使之成为一套具有简单逻辑性的体系. 根据各种方法的特点,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 G ao chang Directed by Associate Prof . Lou Xijuan Abstract Harmonic series is the mathematical analysis ofa 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 II license different. K ey words Harmonic s Series Divergency D iscriminate 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...................................................................................................................