递推数列通项求解策略

摘要：数列是初等数学与高等数学的衔接之一，并且也是高中教学的重点内容，而求数列的通项公式就是其中最为常见的题型之一，既可考察学生的等价转化与化归这一数学思想，又能反映考生对数列理解的深度，具有一定的技巧性．而且近几年的数学高考命题都以数列递推式为内容作为能力型试题，解法灵活，而且能力要求高．等差数列与等比数列是递推数列的特殊情形，对于其他的递推数列，可考虑根据题目的特点，采用归纳法、转化法、构造法、待定系数法等方法，来解决问题．本文介绍几种常用的求递推数列通项公式的方法，以便学生能更快的解决有关递推数列的问题．
关键词：递推数列；求解方法；等差数列；等比数列
Recurrence Formula Solution Strategies
Abstract: Sequence of number is elementary mathematics and the higher mathematics linking up one of , being also senior middle school teaching priority emphasis, ask the sequence of number the formula of general term to be to inscribe one of type among them be common most but, now that may inspect student's equivalence conversion and melt be this responsibility one mathematics method, to be able to reflect the depth that the examinee understands to progression , have the certain dexterity. The mathematics the past few years college entrance examination proposition all takes that progression recursion is dyadic as content and nimbly as ability type examination questions , method of solving , the ability demands height and. Arithmetic sequence of number and geometric sequence of number are recurrence sequence of number progression circumstance, solves a problem the past such as adopt induction , changing law , structure law , method of undetermined coefficient . The several kinds demand recursion in common use progression the main body of a book is introduced exchanges item formula method, for the purpose of the student can resolve problem about recursion progression more quickly.
Keywords: Recurrence formula; Find the solution; Arithmetic sequence of number; Geometric sequence of number

 
目　　录

1 递推数列的定义................................................2
2 六种求解方法..................................................2
  2.1 归纳法....................................................3
  2.2 转化法....................................................5
  2.3 构造法....................................................6
  2.4 待定系数法................................................8
  2.5 叠加法....................................................9
  2.6 换元法....................................................10
参考文献........................................................13
致谢............................................................14