一个新的正项级数敛散性的判别法.pdf

第34 卷第2 期 唐山师范学院学报 2012 年3 月 Vol.34 No.2 Journal of Tangshan Teachers College Mar. 2012 一个新的正项级数敛散性的判别法 顾先明，彭 浩 （唐山师范学院 数学与信息科学系，河北 唐山 063000 ） 摘 要：用级数  1 n lnp n n 2 做比较标准，得到一个比拉阿比判别法更为精细又应用方便的判别法，称为“对数判别法”。 关键词：比较判别法；级数判别法的极限形式；Lagrange 中值定理；对数判别法 O173 A 1009-9115(2012)02-0031-03 中图分类号： 文献标识码： 文章编号： A New Criterion of the Convergence and Divergence of the Positive Series GU Xian-ming, PENG Hao (Department of Mathematics and Information Science, Tangshan Teachers College, Tangshan 063000, China) Abstract: In this paper, a new criterion was proposed to discriminate the convergence of positive series by using series  1 n lnp n n 2 as a comparing standard. This type of criterion is finer and more convenient than that frequently-used Raaba’s criterion. Key Words: new criterion; positive series; ponvergence; Raaba’s criterion 1 引言