一个重要极限多种证法的教学反思

Teaching Infrospection of Many Testimonies on an Important Limitation

在数学分析教学中,曾经用"ε-N"语言证明了数列极限limn→∞n/na=0(a>1),但是在许多具体的计算或者证明中又需要将该极限推广到limn→∞nk/an=0(a>1,k为正整数),怎样引导高年级学生对推广后的极限进行证明,成为了课堂教学的重点和难点.

In the teaching of mathematical analysis, number sequence limitation— lim^n /a^n= 0 （a 〉1） --has once been testified to in ＂ e-N language. However,it should be generalised to number sequence limitation-- lim n^λ/a^n = 0 （a 〉 1 ,k ∈ N ） in more calculations or testimonies. How to elicitate upper students to testify to the generalised limitation remains important and difficult in classroom teaching.