查人人中国名人网boss直聘招聘版:数学专业翻译
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无穷级数是数学分析及应用中最重要的研究工具之一。
判别无穷级数的收敛与发散一直是数学中大家关注的问题。
本文准备研究判别正项级数收敛与发散的一种新的判别法。
显然这个研究，不但从理论上，还是在应用上，都是很有意义的。
通常正项级数的敛散性归结于部分和数列的有界性，即正项级数收敛的充要条件是部分和数列有界。
但用部分和数列的有界来判别级数的敛散性在使用上不方便。
本文介绍一个很有用的库默尔(kummer)判别法,由这个判别法可导出达朗贝尔判别法，拉贝判别法，伯尔特昂判别法，高斯判别法等常用的判别法。
infinite series 无限级数；无穷级数
收敛与发散Convergence and Divergence
判别Discriminant
正项级数（positive series）
充要条件necessary and sufficient condition
有界性boundness
d'alembert's Discriminant达朗贝尔判别法
Infinite series is the most important reseach tool in mathematical analysis and application, and discriminant of convergence and divergence of infinite series is generally the problem been paid much attention. This paper prepare to study a new discriminant method for discriminant of convergence and divergence of positive series. It is remarkable that this study is significance in both theory and application.
Generally, the convergence and divergence of positive series depends on the boundness of partial adding sequence ，that is to say, the necessary and sufficient condition for convergence of positive series is that partial adding sequence having bound.
But using the boundness of partial adding sequence to discriminate
the convergence and divergence of series in inconvenient. We introduced useful kummer estimation in this paper, which could detrude d'alembert's Discriminant，La Bell's Discriminant，伯尔特昂Discriminant，Gauss Discriminant etc.