论文部分内容阅读
1~2+2~2+…+n~2=1/6n(n+1)(2n+1)公式在90年代高中数学代数教材的封面上出现,可见是很重要的。它给当时正在上高中的笔者带来了一个很大的疑惑,他是怎么来的呢?直到学习了数列的有关知识后才知道可以用数学归纳法证明,还是无法推导。但是新课程没有提及,但是学习微积分时又离不开它,是因为它的证明过于复杂,还是……?现将笔者对其证明的探究结果展示如下,供读者参考。
It is very important to see that the formula 1 ~ 2 + 2 ~ 2 + ... + n ~ 2 = 1 / 6n (n + 1) (2n + 1) appears on the cover of the mathematical algebra textbook for high schools in the 1990s. It brought a great doubt to the author who was in high school at that time. How did he come from? Until after he learned the knowledge about the series, he knew it could not be proved by mathematical induction. However, the new course did not mention it, but it can not be separated from it when learning calculus because its proof is too complicated or is it? Now, the author’s inquiry into his proof is shown below for reference.