哈尔滨学院本科毕业论文(设计)题目：正项级数敛散性判定的探讨院（系）理学院专 业数学与应用数学年 级2008 级姓 名岳红玉学 号08031324指导教师徐亚兰职 称副教授2012 年 5 月 30 日哈尔滨学院本科毕业论文（设计）目 录摘 要.1ABSTRACT.2前 言.3第一章 正项级数的概念及敛散性的一般判别原则.41.1 级数的相关概念.41.1.1 级数的定义.41.1.2 部分和的定义.41.1.3 收敛与发散的定义.41.1.4 正项级数的定义.41.2 正项级数敛散性判别的充要条件.51.3 三个重要比较级数.51.3.1 几何级数.61.3.2 调和级数.71.3.3 P-级数.7第二章 正项级数敛散性的判别法.92.1 判别发散的简单方法.92.2 比较判别法.92.3 柯西判别法（根值法）.122.4 达朗贝尔判别法（比值法）.142.5 拉贝判别法.172.6 积分判别法.192.7 其它判别法.20第三章 正项级数在生活中的应用.21结束语.23参考文献.24后 记.25哈尔滨学院本科毕业论文（设计）1摘 要正项级数是整个级数内容中的重要组成部分，它的敛散性是级数中最基础的内容。本文通过对正项级数收敛的充要条件进行研究，让读者深刻地理解判定正项10nn nuu级数敛散性的基本方法，在对正项级数收敛的充要条件进行分析的基础上，研究了正项级数敛散性的各种判别法的使用条件。本文主要在比较判别法及其推论、柯西判别法及其推论、达朗贝尔判别法及其推论、拉贝判别法及其推论几方面探讨了正项级数的敛散性。同时还探讨了它们的证明过程及应用其解决相关问题的例题，并简单介绍了它们之间的联系，如强弱性的比较，不同形式的题适合用哪种方法来证明其敛散性更为简单。最后通过举例说明了正项级数敛散性的判别法在判别级数敛散性中的作用。关键词关键词:正项级数；比较判别法；柯西判别法；达朗贝尔判别法；拉贝判别法哈尔滨学院本科毕业论文（设计）2ABSTRACTPositive series is an important series in the series content, its convergence and dispersion is the most basic content of series. Through going deep into studying the full and necessary condition of positive series, the paper profoundly understands and judges the basic method of the convergence and dispersion of positive series, and studies all kinds of judging methods condition of maintenance. The paper principally probes into the convergence and dispersion of positive series in the compare judging method and inference, Cauchy judging method and inference, D Alembert judging method and inference, and Raabe judging method and inference. At the same time, it inquires into their proving process and applies them to solve relating examples, introduces simply the relation among them, such as the strong and weak property compare. Which method of proving different form judging methods is the easiest? Finally the paper introduces the function of the positive series convergence and dispersion judging methods in the series convergence and dispersion judgment.Key words:positive series; compare judging method; Cauchy judging method; D Alembert judging method; Raabe judging method哈尔滨学院本科毕业论文（设计）3前 言数学分析作为数学系的重要专业基础课程，对学习好其他科目起着至关重要的作用。同时级数又是数学分析的重要