有关自然数的有限项幂和

Sums of Finite Terms of Powers of Natural Numbers

仅用幂函数的求导和积分的形式运算公式和初等的方法求出了自然数有限项幂和当幂为非负整数时的求和公式。同时,又用函数的泰勒级数展开求出了自然数有限项幂和,当幂为非整数且大于—1的实数时,有一个关于R的系数不变的幂函数和的逼近,且是一个1/R的正数阶逼近。

This paper gives the formulas of the sums when the power is non-negative integers through the derivation and integration of the power function and by using the elementary method. The approximations of fixed coefficient power functions are alse given when the power is non-integer real numbers and over-1.