克莱姆法则与矩阵的初等变换在自然数幂和问题中的应用

Cramer's Rule and Elementary Transformation of Matrix for Sum of Powers of Natural Numbers

本文在矩阵的辅助下,运用初等变换的技巧,从三个不同的方面研究了自然数的幂和问题.通过构造矩阵方程,分别使用克莱姆法则、初等变换、递推关系分析了自然数幂和问题的和式结构,并给出了三种不同类型的解析表达式.

In this paper,by constructing matrix equations and using Cramer's rule,elementary transformations and recursion relations,the problem of sum of powers of natural numbers is discussed from three different aspects.