线性递推关系数列极限的求法

A method for calculating the limit of linearrecursive relation sequence

首先,探讨Fibonacci数列通项比的极限,并推广到一般线性递推关系通项比的极限,然后,根据条件p+q=1及通项比极限,求得具有一般线性递推关系式数列极限公式,可以直接用此极限公式解决一些极限问题,最后,探讨分式线性关系数列极限的求解,发现也可以推导出其求极限的公式。在探讨各类线性递推关系数列极限的求解方法时,给出了具体求极限的案例进行分析,为极限的学习和教学提供参考。

First,we discuss the limit of the general term ratio of Fibonacci sequence,and extend it to the limit of the general term ratio of general linear recurrence relation.Then,according to condition p+q=1 and the limit of the general term ratio,we can obtain the limit formula of sequence with general linear recurrence relation.We can directly use this limit formula to solve some limit problems.Finally,the solution of the limit of fractional linear relation sequence is discussed,and it is found that the formula of the limit can also be derived.And when discussing the solution methods of the limit of various linear recursion relations,it gives specific cases to analyze the limit,which provides reference for limit learning and teaching.