求高阶差等比数列通项的公式解法  

A Formula Method for the General Term of a Sequence with Higher Order Differences to be a Geometric Sequence

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

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：《高等数学研究》2024年第1期69-71,共3页Studies in College Mathematics

摘　　要：通过对高阶差等比数列通项公式的构成形式进一步研究,得到了该类数列通项公式的标准形式.并利用矩阵的初等变换以及差分的方法导出了求该数列通项公式中各系数的计算公式,从而得到了求高阶差等比数列通项公式及前n项和的一种公式解法.By applying the method of successive difference to a sequence of numbers,an equal-ratio sequence is obtained after several order differences.This sequence is also called the equal-ratio sequence of higher order differences.In this paper,the general term and the formula of the sum of the preceding term of the equal-ratio sequence of higher order differences are obtained by using the method of matrix only,thus solving the problem of summing the general term and the preceding term of the equal-ratio sequence of higher order differences.

关 键 词：逐差法 高阶差等比数列 差分法 

分 类 号：O155[理学—数学]