一个重要极限多种证法的教学反思 |
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引用本文: | 胡其明.一个重要极限多种证法的教学反思[J].大学数学,2011,27(5):195-199. |
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作者姓名: | 胡其明 |
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作者单位: | 贵州省兴义民族师范学院数学系,贵州兴义,562400 |
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摘 要: | 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.
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关 键 词: | 极限 海涅定理 洛必达法则 收敛级数 斯笃茨定理 |
Teaching Infrospection of Many Testimonies on an Important Limitation |
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Abstract: | 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. |
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Keywords: | limitation Heine theorem L Hospital rule restrictive progression Stolz theorem |
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