| 一类正项级数收敛性的一个刻画及其应用 |
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| 引用本文： | 许绍元. 一类正项级数收敛性的一个刻画及其应用[J]. 吉首大学学报(自然科学版), 2018, 39(3): 1. DOI: 10.3969/j.cnki.jdxb.2018.03.001 |
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| 作者姓名： | 许绍元 |
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| 作者单位： | （韩山师范学院数学与统计学院，广东 潮州 521041） |
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| 基金项目： | 广东省本科高校教学质量与教学改革工程项目(粤高教函〔2015〕133号) |
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| 摘 要： | 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.
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| 关 键 词： | 正项级数 数列 收敛性 |
Characterization of Convergence of a Class of Series with Positive Terms and Its Applications |
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| XU Shaoyuan. Characterization of Convergence of a Class of Series with Positive Terms and Its Applications[J]. Journal of Jishou University(Natural Science Edition), 2018, 39(3): 1. DOI: 10.3969/j.cnki.jdxb.2018.03.001 |
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| Authors: | XU Shaoyuan |
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| Affiliation: | (School of Mathematics and Statistics,Hanshan Normal College,Chaozhou 521041,Guangdong China) |
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| Abstract: | 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. |
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| Keywords: | series with positive terms sequence of numbers convergence |
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