关于幂级数逐项积分的积分下限的讨论

Discussion about the Lower Limit of the Integral of Termwise Integration Power Series

求幂级数和函数的方法与技巧是多种多样的,它的难度较大、技巧较高,对学生来说是一个难点,其中利用逐项积分法计算幂级数和函数的方法,学生在学习时,对积分下限选为0感到困惑,本文讨论了积分下限选为0的原因和积分下限的选取范围。

Methods and techniques of calculating power series and function are diverse. It is a more difficult and higher skillful task for students. In the method for calculating the power series sum function, there is an interesting method of using the termwise integration. The students are confused about the lower limit of the integral selected as 0 in this method. This article discussed the reasons of the lower limit of integration is selected as 0 and the selectting scope of the lower limit of integration.