正项级数对数判别法的一种推广形式  

An improved positive series logarithmic discriminant method

作　　者：刘璟现 张玥 张玉林 LIU Jing-xian;ZHANG Yue;ZHANG Yu-lin(College of Mathematics and System Science,Shandong University of Science and Technology,Qingdao 266590,China)

机构地区：[1]山东科技大学数学与系统科学学院

出　　处：《高师理科学刊》2019年第11期9-12,共4页Journal of Science of Teachers＇College and University

基　　金：山东科技大学青年教师教学拔尖人才培养计划资助项目(BJRC20180502);山东科技大学教学群星计划项目(QX2018M26)

摘　　要：对于正项级数∑n=1^∞un,∑n=1^∞vn,依据un+p/un≤vn+p/vn,给出并证明了推广的比值判别法;基于通项(un/un+p)^n/p的取值,得到了正项级数对数判别法一种推广的极限形式,并将其应用于判定交错级数的绝对收敛或条件收敛,给出并证明了相关定理.通过2个实例验证了推广方法的有效性.For positive series∑n=1^∞un,∑n=1^∞vn,the generalized ratio discriminant method is given and proved based on un+p/un≤vn+p/vn,then on the basis of(un/un+p)^n/p,the generalized logarithmic discrimination method and its ultimate form are given.It is applied to determine the absolute convergence or conditional convergence of staggered series,and the relevant theorem is proved.Finally,the validity of the method is verified by two examples.

关 键 词：正项级数 比值判别法 对数判别法 

分 类 号：O173[理学—数学]