| 正项级数的Gauss指标判别法 |
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| 引用本文： | 姬小龙,王锐利.正项级数的Gauss指标判别法[J].数学的实践与认识,2008,38(11):207-209. |
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| 作者姓名： | 姬小龙 王锐利 |
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| 作者单位： | 济源职业技术学院,基础部,河南,济源,454650 |
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| 摘 要： | 在正项级数Gauss判别法的基础上,定义了正数列an的Gauss指标G=limn ln(an/an+1)-1]ln n.从而得到了正项级数的Gauss指标判别法.通过具体计算已有各种判别法的Gauss指标,结果表明,Gauss指标判别法是达朗贝尔、柯西、拉贝、高斯和Bertrand等5种判别法的推广.
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| 关 键 词： | 正项级数 Gauss判别法 Gauss指标 |
| 修稿时间： | 2008年1月5日 |
The Gauss Index Discrimination Method of Positive Term Series |
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| JI Xiao-long,WANG Rui-li.The Gauss Index Discrimination Method of Positive Term Series[J].Mathematics in Practice and Theory,2008,38(11):207-209. |
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| Authors: | JI Xiao-long WANG Rui-li |
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| Abstract: | Based on the Gauss discrimination method of positive term series,this paper defines the Gauss index G=limn ln(an/an+1)-1]ln n of Positive number sequence an and gains the Gauss index discrimination method of positive term series.What′s more,it is proved that the Gauss index discrimination method is on the basis of the J.D′ Alembert′s criterion, the A.L.Cauchy′s criterion and the Gauss criterion and the Bertrand′s criterion etc.through calculating all the Gauss index discrimination methods. |
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| Keywords: | positive term series Gauss discrimination method Gauss index |
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