利用方阵幂的计算探讨递归数列x_(n+1)=ax_n+b/cx_n+d的周期性

Probe into the periodicity of recursive sequence x_(n+1)=ax_n+b/cx_n+d by adopting the calculation of square matrix power

本文利用方阵幂的计算,探讨了递归数列x_(n+1)=ax_n+b/cx_n+d的周期性,并得到了其数列的通项公式。

This paper utilizes the calculation of matrix power to explore the periodicity of recursive sequence x_(n+1)=ax_n+b/cx_n+d and then gains its formula of general term.