求等差数列前n项等幂和的若干公式

A NEW FORMULA FOR EVALUATING THE SUM OF d-th POWERS OF THE FIRST n TERMS OF AN ARITHMETIC SEQUENCE

本文利用Ｂｅｒｎｏｕｌｌｉ数，给出可以精确到任意阶的等差数列前ｎ项等幂和的表示公式，并导出了（ｎ为偶数）的不含常数项的ｎ的多项式表示式．

This paper, by using Bernoulli numbers, gives a new formula for evaluating (a, d > 0, α∈R), which may be accurate in arbitary order, and represents both (q is a positive integer) to polynomials of n with no constant.