求自然数幂和的差分算子法  

The Difference Operator Method for the Sum of Powers of Natural Numbers

作　　者：戴中林[1] DAI Zhong-lin(School of Mathematics and Information, Xihua 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》2020年第4期117-121,共5页College Mathematics

摘　　要：给出了求自然数幂和的差分算子解法,即先用待定系数法表出自然数幂和的有限项形式,即幂和多项式,然后建立以待定系数为未知量的线性方程组,通过应用矩阵初等变换以及差分算子的计算方法,最后求得确定幂和多项式各待定系数的解矩阵,从而得到求自然数幂和的又一种计算方法.The difference operator solution for the sum of powers of natural numbers is given,that is,the finite term form of the sum of powers of natural numbers is expressed by the method of undetermined coefficients,and then the linear equation system with undetermined coefficients as the unknown quantity is established.By using the elementary transformation of matrix and the calculation method of difference operators,the solution matrix of undetermined coefficients of powers and polynomials is finally obtained,so as to obtain the sum of powers of natural numbers a calculation method.

关 键 词：自然数幂和 幂和多项式 差分算子 解矩阵 

分 类 号：O155[理学—数学]