求自然数幂和的差分公式法  

Difference Method for Sums of Powers of Natural Numbers

作　　者：戴中林[1] DAI Zhonglin(School of mathematics and information,China West Normal University,Nanchong,Sichuan 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》2020年第4期29-31,共3页Studies in College Mathematics

摘　　要：给出了求自然数幂和的一种差分公式法.首先将自然数幂和表示为有限项多项式形式,且每一项为关于自然数n的递减连乘积,由此建立以各项系数为未知量的线性方程组,并通过应用矩阵初等变换以及差分算子的计算工具,从而得到求自然数幂和的又一计算公式.In this paper, the difference method is used to obtain a formula for a sum of powers of natural numbers. The process involves expressing such a sum as a polynomial with each term being the product of decreasing natural numbers, establishing a linear system of equations with each coefficient as an unknown quantity, and solving the linear system by the elementary transformations and the difference method.

关 键 词：自然数幂和 差分算子 公式解 

分 类 号：O151.2[理学—数学]