一类正项级数收敛性的一个刻画及其应用

摘要

We prove the characterization of the convergence of a class of series with positive terms can be conducted by the convergence of a relevant monotone positive sequence.Based on some questions in the preliminary contest of National College Student Mathematics Competitions and some questions in the"mathematical analysis" of the graduate entrance examination ,some examples are provided to illustrate the applications of the results in solving the problems of series convergence .%证明了一类正项级数收敛性的一个刻画是与之相关的单调正数列的收敛 .结合中国大学生数学竞赛预赛(数学类)试卷和硕士研究生入学考试数学分析试卷的部分试题,举例说明了主要结果在处理一类级数收敛问题中的应用 .