p-级数收敛性积分证明的几何方法

The Geometric Method to Demonstrate Convergence of p-series with Integration

借助无穷区间上的反常积分证明P-级数的收敛性是一种比较有效的方法,但因其证明过程相对比较抽象而不易被学生所接受.借助积分的几何意义和元素法的基本思想构建其证明思路与过程,则更直观、简洁,在教学与学习过程中能够起到事半功倍的效果.

To demonstrate the convergence of p -series with the improper integral on infinite interval is a relatively affective way. But the proof is relatively abstract and difficult to be understood by students. This paper suggests the teaching method of constructing the idea and process of the proof with the geometric meaning of integration and the idea of the element method. This method, which is more intuitive and concise, can improve the teaching and learning of p -series and p -integration.