The sum of the squares of the first n natural numbers: two different but similar approaches, and a bonus

被引：0

作者：

Grima, Pere ^{[1
]}

Marco, Lluis ^{[1
]}

机构：

[1] Tech Univ Catalonia UPC, Dept Stat & Operat Res, Barcelona, Spain

来源：

INTERNATIONAL JOURNAL OF MATHEMATICAL EDUCATION IN SCIENCE AND TECHNOLOGY | 2008年 / 39卷 / 02期

关键词：

D O I：

10.1080/00207390701458578

中图分类号：

G40 [教育学];

学科分类号：

040101 ; 120403 ;

摘要：

This note presents two demonstrations of the known formula for the sum of squares of the first n natural numbers. One demonstration is based on geometrical considerations and the other one uses elementary integral calculus. Both demonstrations are very easy to understand, even for high school students, and may be good examples of how to explore ways to demonstrate a formula by induction. Finally, it is explained how to deduce the formula using a simple spreadsheet.

引用

页码：233 / 238

页数：6

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