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在贵刊2001年2月上期及2001年12月上期上,分别刊登了谢秀英与张立华二位老师的关于导出12+22+32+…+n2(设为Sn)的公式的几种方法,很受启发.笔者在这一部分的教学过程中,与学生一起发现了12+22+32+…+n2的公式导出的另外一种方法. 看图1的数阵:可以看作是一个“等边三角形”,其共有n行,每行的数字相同(从上至下每一行的数都是这一行的行数,且每一行数的个数与行数也相同).不难看出每行所有数的和分
In the last issue of your magazine in February of 2001 and the last issue of December 2001, several methods for formulating the formulas of 12+22+32+...+n2 (as Sn) by Xie Xiuying and Zhang Lihua were published. Inspired. In the teaching process of this part, the author discovered with the students another method of formulating the formula of 12+22+32+...+n2. Looking at the array of Figure 1, it can be seen as an “equilateral”. Triangles, which have a total of n rows, each with the same number (the number of rows from top to bottom is the number of rows in this row, and the number of rows and the number of rows per row is also the same). It is not difficult to see that each row has all The sum of numbers