窥递推法之隐情,释组合式之深义

• 作 者: 杨洁
• 机 构: 浙江省宁波市鄞州中学,
• 出 处: 中学数学教学参考
• 发表日期: 2017年Z3期
• 关键词: 递推法 组合恒等式 数学问题 二项式反演 容斥原理 思维创新 通项公式 记法 正整数 非负整数

一般地,与递推式和组合恒等式有关的数学表达式在形式上复杂,看似难以记忆,然其本身往往蕴含着奇妙的实际背景意义。本文从一道例题出发,引导学生进行不断的思维创新,并在此基础上进行深入思考,搭建数学问题分支间的桥梁,以期达到激发兴趣,由点及面,开拓视野的效果。1窥递推法之隐情题目:n,k∈Z’且n≥k。以g(n,k)表示把n件

In general, mathematical expressions related to recursion and combinatorial identities are complex in form and appear to be hard to memorize. However, they often contain fantastic actual background meanings. This article starts from a case study, guides the student to carry on the constant innovation of thinking, and on this foundation carries on the thorough thinking, builds the bridge between the branches of mathematics problem, in order to achieve the goal which stimulates the interest, the point and the surface, broadens the field of vision. Glimpse of the law of pushing the hidden issues: n, k∈Z ’and n ≥ k. To g (n, k) that n pieces