正项级数收敛性的判别法的进一步研究

A New Convergence Criterion of Positive Term Series

用初等方法深入研究了正向级数判别法,基于比值判别法和根值判别法判别法思想,研究了更高精度判别法,给出不断提高精度的判别法的构造思想以及一般性定理。

Using elementary methods,the positive series judge method In-depth is studied,Based on the idea of Ratio test and the root value based identification method,this paper gives a new and more exact criterion.Furthermore,it proposes a general idea to construct a series of criterions with increasing precision.By the way,it proves that there is no ＂best criterion＂ that can judge every series by comparing the quotient of adjacent terms,or there is no positive term series that have the lowest ＂speed＂ of convergence.