新探级数收敛的判别方法

新探级数收敛的判别方法

摘 要

本给出了级数收敛判别的几种新方法.（1）隔项比值判别法:它较比式判别法更精细.用比式判别方法可以判别的级数,用隔项比值判别法可以判别,用隔项比值判别法可以判别的级数,却不1定能用比式判别法判别,即隔项比值判别法应用更广泛,但也更复杂些;（2）以调和级数为比较对象的比较判别法:在 级数中,当 时,级数收敛,当
时,级数发散,当 =1时,即为调和级数,它为收敛与发散的分界点;（3）阿贝尔判别法的推广:阿贝尔判别法中,改变它的条件,得到新的判别方法;（4）函数判别法:该判别方法的包容性很强,只要适当的选取满足条件的函数,则可以得到1些具体的判别方法,即该方法为1些具体方法的普遍公式.
关键词:级数; 收敛; 发散; 判别法

Probe the Criterion of the Convergence for Series Newly

ABSTRACT

This paper has introduced several new criterions for the convergence of series. The first one is gap ratio criterion: It compares the ratio criterion to be finer. The gap ratio criterion can differentiate all the series that can be differentiated by the ratio criterion , but the series that can be differentiated by the gap ratio criterion, not necessarily can use the ratio actually to differentiate, namely the gap ratio criterion is much more widely used, but more complicated. The second one is comparison criterion which take harmonic series as the comparison object: When , the  -series converges, When , the  -series diverges. When, the  -series names harmonic series .it is the dividing line of convergence and divergence. The third criterion is the promotion of Abel criterion: If we change the conditions of the Abel criterion, we will obtain some new criterions. The fourth criterion is function criterion: the capacity of this criterion is very strong, so long as we select the suitable functions that satisfy its conditions, we will obtain some concrete criterions. This criterion is a universal formula. （转载自http://www.ＮＳＥＡＣ.com中国科教评价网）
Key words: series; convergence; divergence; criterion

目 录

中文标题-----------------------------------------------------------------------1
中文摘要、关键词---------------------------------------------------------------1
英文标题-----------------------------------------------------------------------1
英文摘要、关键词----------------------------------------------------------------2
前言---------------------------------------------------------------------------3
正文---------------------------------------------------------------------------4
1 基本概念和定理----------------------------------------------------------------4
2 隔项比值判别法----------------------------------------------------------------5
3 以调和级数为比较对象的比较判别法-----------------------------------------------11
4 阿贝尔判别法的推广------------------------------------------------------------13
5 函数判别法-------------------------------------------------------------------16
6 结束语-----------------------------------------------------------------------18
参考文献-----------------------------------------------------------------------20
致谢---------------------------------------------------------------------------21

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