等差数列前n项等幂和计算公式及算法实现

Calculation Formula of the Sum of Powers of the First n Terms of an Arithmetic Sequence and Its Algorithm

首先利用微分算子以及Bernoulli数巧妙地得到了求任意等差数列前n项等幂和的一个简洁且更一般的计算公式,同时利用导出公式分别给出了前n个自然数等幂和公式和前n个奇数的等幂和公式,然后利用Maple7给出计算程序.

At first, the paper gives a general formula of the sum of powers of the first n terms of any arithmetic sequence using the differential operator and the Bernoulli numbers, specifically gives the Sum of powers of the first n natural numbers and first n odd numbers, and then presents a calculating program of the general formula.