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数列问题中由递推公式求通项公式的题目屡见不鲜,我们曾经学过一些方法,如累加累乘、配凑法等,但是这些方法能解决的题型有限,而且不一定就是最简单的.下面笔者为大家介绍两种方法:特征方程法和待定系数法.一、特征方程求通项公式先以一道题为例.例1已知a_(n+2)=5a_(n+1)-6a_n,a_1=0,a_2=1,求a_n.步骤1设特征方程x~2=5x-6,其中x~2对应a_(n+2),5x对应5a_(n+1),-6对应-6a_n.
There are many problems in the series of problems that are solved by the formula of recursion formulas. We have learned some methods, such as accumulation and multiplication, and co-ordination methods. However, the problems that these methods can solve are limited and not necessarily the simplest ones. Here I introduce two methods for everyone: the eigenvalue method and the coefficient to be determined. First, the eigenvalue equation to get through the formula of a problem for example. Example 1 Known a_ (n +2) = 5a_ (n +1) - Step 1 Let eigenvalue x ~ 2 = 5x-6, where x ~ 2 corresponds to a_ (n + 2), 5x corresponds to 5a_ (n + 1), - 6 corresponds -6a_n.