高阶差等比数列通项公式的矩阵解法  

The Matrix Solution to the General Term Formula of Higher Order Difference Equal Ratio Sequence

作　　者：戴中林[1] DAI Zhonglin(School of Mathematics and Information,West China Normal University,Nanchong Sichuan 637002,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637002

出　　处：《大学数学》2022年第1期107-112,共6页College Mathematics

摘　　要：通过对高阶差等比数列的通项公式深入研究,发现可将该通项公式设为与等差数列及等比数列通项公式相关的标准形式,基于矩阵变换及差分算子的思想,得到了求通项公式中各系数的解矩阵.从而给出了高阶差等比数列通项公式及前n项和的一种新方法.If the difference by difference method is applied to a positive integer sequence,an equal ratio sequence can be obtained,then the original sequence is called higher order difference equal ratio sequence In this paper,through the in-depth study of the general term formula of higher-order difference and equal ratio sequence,it is found that the general term formula can be set as a form related to the general term formula of equal difference and equal ratio sequence,and the solution matrix of the coefficients of the general term formula is obtained by using the mathematical methods of matrix transformation and difference operator.Thus another new solution method of the general term formula and the sum of the preceding terms of higher-order difference and equal ratio sequence is given.

关 键 词：逐差法 等比数列 通项公式 解矩阵 

分 类 号：O155[理学—数学]