无穷级数的发展历程

无穷级数理论是高校数学专业《数学分析》课程和理工科专业《高等数学》课程中的重点和难点,学生理解和掌握相对困难,教师想要解决这一问题,根据HPM理论,一个好的方法是了解其发展的历史脉络,本文理清了无穷级数理论的萌芽、发端和成熟的历程,从逃避无穷到区分并能够证明收敛和发散,最后以新的可和性理论对级数理论进行新的划分。把这些素材应用到相应的教学中去可以激发学生学习的兴趣、提高其学习效果,感受数学的文化价值。

It is important and difficult to catch that the infinite series theory in mathematical analysis or advanced mathematics , students couldn＇t understand： and catch it smoothly, we can study the history of infinite series to help our students and improve our teaching effectiveness. So the simple history of infinite series was straighten up in this paper, from the initial stage of it to the sum of divergent series. All of this could be used in the teaching of the college＇s teacher.