浅谈级数的应用与一点注记  

On Application of Infinite Series and Power Series

作　　者：宋洪雪[1] 邱中华[1] 丁秀梅[1] SONG Hongxue;QIU Zhonghua;DING Xiumei(College of Science,Nanjing University of Posts and Telecommunications, Nanjing,Jiangsu 210023, PRC)

机构地区：[1]南京邮电大学理学院,江苏南京210023

出　　处：《高等数学研究》2018年第3期30-35,共6页Studies in College Mathematics

基　　金：国家自然科学基金(11401165;61503198);南京邮电大学教改项目(JG00716JX28)

摘　　要：该文通过对八个示例的分析及求解,介绍了级数在不等式证明、求高阶导数、计算一类定积分、解微分方程等四个方面问题中的应用.并简单介绍了综合利用数列极限理论和微分方程等工具研究幂级数的收敛域与和函数的方法和技巧.By the examinations of eight typical examples,this paper summarizes the application of infinite series in provinginequalities,finding higherorder derivatives of functions,calculating definite integrals,and solving the differential equations.It also introduces the methods and techniques for the convergence domains and sum functions of power series by using the tools of limit of sequence and differential equation.

关 键 词：无穷级数 高阶导数 积分 不等式 幂级数 

分 类 号：O173[理学—数学]