——浅析递推关系在高中数学应用.docVIP

编号： 本科学生毕业设计（论文） 题 目： 浅析递推关系在高中数学的应用 系部名称： 数 学 系 专业名称： 数学与应用数学 摘 要ABSTRACT Everything in the word we inadvertently quietly changing, in numerous changes, many phenomena are regular. This rule often showing the antecedents and consequences of the relationship, we can use the recursive thinking to study these changes. The paper first Fibonacci rabbit problems introduced a simple solution to the rabbit problem Fibonacci sequence, then emphatically introduces the recursive relation in solving sequence passes a formula in the building process and the solving method, final illustrate recursive relation in the high school mathematics probability, permutation and aspects of the application. According to the passage to establish recursion, analysis the recursion method, learn recursion relations for the flexible characteristic. As in solving the sequence passes a formula usually differential superposition method, general substitution method, recursive solution. At the same time, make it into our real life, we often encounter some practical solutions. As the recursion relation for the development and research, has formed the quite many types. The type of in-depth research, let the applications of recurrence relation is more convenient; make its more extensive applications. Keywords: Recursive relations; high school mathematics; sequence; the formula of general term 第一章 引言 1 第二章 递推关系的起源与发展 2 2.1 斐波拉契数列的萌芽 2 2.2 斐波拉契数列的简介 2 2.2.1 斐波拉契数列定义及递推公式 3 2.2.2 斐波拉契数列的通项公式 3 2.2.3 斐波拉契数列的几个特性 3 2.3 大自然中的斐波拉契数列 4 第三章 递推关系求数列的通项 5 3.1 一阶递推数列 5 3.1.1 一阶线性递推数列 5 3.1.2 一阶非线性递推数列 6 3.2 二阶递推数列 8 3.2.1 二阶齐次线性递推数列 8 3.2.2 二阶齐次非线性递推数列 9 3.3 分式递推数列 10 第四章 递推关系在其他方面的应用 11 4.1 递推关系在概率中的应用 11 4.2 利用递推关系求解排列组合问题 12 4.3 在数学归纳法中寻找递推关系 13 4.4生活中的递推关系 14 结束语 15 参考文献 16 致谢 17 第一章 引言 递推思想作为数学里的一种重要思想，体现了世界上众多事物所蕴含的现象、变化及其遵循的一种前因后果的关系.在众多的数学分支如：数列、排列组合、概率等中起着至关重要的作用，存在着非常广泛的应