求自然数的m(m∈N)次等幂和Sm(n)=∑nk=1km是一个著名而有趣的数学问题,它最先出现在1713年出版的瑞士数学家j.柏努利(1654-1705)的一部著作中[1],历史上曾有不少的数学家也研究过它的解法,现仍有中学老师研究它的解法[2].最近,在某师范大学的教育硕士生的课堂上以“求S2(n)=∑nk=1k2”为案例进行了课堂交流,在该堂课上教育硕士们共给出了此问题的八种初等解 It is a well-known and interesting mathematical problem to find the natural powers of m (m∈N) and Sm (n) = Σnk = 1km, which first appeared in 1713 by the Swiss mathematician J. Bernoulli (1654 -1705) [1], there have been many mathematicians in history who have studied its solution, there are still high school teachers to study its solution [2] .Recently, in a normal university education master Students in the class conducted a class exchange in the case of “S2 (n) = Σnk = 1k2 ”, in which eight master’s solutions were given by the Master of Education