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计算前n个自然数的方幂和的方法,在国内书刊上已有介绍(例如,上海教育出版社的《初等数学论丛》第7辑上就有《计算自然数的方幂和的一种方法》一文).这些文章所介绍的方法,大多采用“递推”方式给出的,即是,欲求前n个自然数的m次方幂和,得先算出前n个自然数的1次方幂和,2次方幂和……,m—1次方幂和,在此基础上,再用所述方法计算m次
The method for calculating the sum of the powers of the first n natural numbers has been introduced in domestic publications (for example, the 7th series of “Elementary Mathematics Forum” of Shanghai Education Press has a method for calculating the sum of squares of natural numbers. “The article”. Most of the methods described in these articles are given in a “recursive” manner. That is, for the m-th power sum of the first n natural numbers, the 1st power sum of the first n natural numbers must be calculated first. , 2nd power and ..., m-1 power sum, on this basis, and then calculated by the method m times