根据递推公式,求数列通项公式的常用方法总结归纳

求递推数列通项公式的常用方法归纳 目录 一、概述 ·································· 二、等差数列通项公式和前 n 项和公式 ·································· 1 、等差数列通项公式的推导过程 ································ 2、等差数列前 n 项和公式的推导过程 ·································· 三、一般的递推数列通项公式的常用方法 ·································· 1、公式法 ·································· 2、归纳猜想法 ·································· 3、累加法 ·································· 4、累乘法 ·································· 5、构造新函数法(待定系数法） ·································· 6、倒数变换法 ·································· 7、特征根法 ·································· 8 、不动点法 ································· 9 、换元法 ································· 10、取对数法 ·································· 11、周期法 ·································· 一、概述 在高中数学课程内容中，数列作为离散函数的典型代表之一，不仅在高中数学中具有重要位置，而且，在现实生活中有着非常广泛的作用，同时，数列的教学也是培养观察、分析、归纳、猜想、逻辑推理以及运用数学知识提出问题、分析问题和解决问题的必不可少的重要途径。 数列这一章蕴含着多种数学思想及方法，如函数思想、方程思想，而且在基本概念、公式的教学本身也包含着丰富的数学方法，掌握这些思想方法不仅可以增进对数列概念、公式的理解，而且运用数学思想方法解决问题的过程，往往能诱发知识的迁移，使学生产生举一反三、融会贯通的解决多数列问题。在...