双比值判别法与对数判别法的比较

The Comparison between Double Ratio Methods and Logarithmic Criteria

双比值判别法是近年来提出的判别正项级数敛散性的一种新方法,它强于传统的达朗贝尔判别法与拉贝判别法.关于双比值判别法与对数判别法的强弱关系问题是值得探讨的.通过对这两种判别法中所含极限的存在性关系的研究,可以得出对数判别法强于双比值判别法的结论.

Double retio method is a new method raised recently to judge convergence and divergence of positive series. It is more powerful than traditional D'Alembert judge method and Laabe judge method. It is worth to consider the ralationship between double ratio method and logarithmic criterion. By studying the relation of the existence of limits in these two criteria. It is proved that the logarithmic criterion is stronger than the double ratio method.