自然数幂求和公式的计算机实现

自然数幂的求和问题 ,一直受到人们的关注 .著名数学家陈景润对此就有过较好的研究 ,更多结果散见其他许多文献 .但都比较烦琐 .本文借助 Mathematica软件 ,利用高阶等差数列的一个结论 :m阶等差数列的充要条件是其前 n项和为 n的 m+ 1次多项式 .给出了一种求自然数幂前 n项和的一种简单方法 .利用此方法还可实现小于 m的自然数幂前 n项和的同时实现 .

The Program of Calculate Formula about Sum of Power of Natural

It is concerned that the sum of power of natural number for a long time. Famous mathematician Chen Jingrun had studied it and a better result. More results can be seen iin other literatures. But all of the results are extraordinary complex. In this paper, authors have a simple method for it by Mathematica software. It is based by one of the result about higher steps arithmetic sequences: a sequence is a m-th-order arithmetic sequence if and only if it is a polynomial of degree m+1 of n. In this paper, we have obtained a series formulas on ∑ni=1ij, jm, m∈N is same time.