对幂级数性质的分析研究

Analysis and Research on the Properties of Power Series

通过对幂级数性质进行分析和例题研究发现,“逐项积分”的解题方法可以转化为“逐项求导”来求解。“逐项积分”和“逐项求导”存在由外向内和由内向外的解题区别,幂级数求和函数也可以利用幂级数的性质结合微分方程的求解方法。

Through the analysis of the characteristic of power series and the study of examples,it is found that the solving method of“taking the integration term by term”can be transformed into“taking the derivative term by term”.The differences of“taking the integration term by term”and“taking the derivative term by term”are outside-in and inside-out.Power series summation function can also be realized through the power series properties combined with differential equation solution method.