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That Ubiquitous Sum: 1 + 2 + 3 + • • • + n

Stanley Bezuszka, Margaret Kenney 

January 2005, Volume 98, Issue 5, Page 316

Abstract:
How the arithmetic series 1 + 2 + 3 + . . . + n is pervasive in mathematical contexts as a powerful problem-solving tool. Algebra students solve the problem with multiple approaches including geometric and creating general equations. Authors discuss the work of Cantor and Gauss in relation to the series.

Keywords:
Article
Cross-Content (Math Only) Connections
Algebraic Patterns
Grades 9-12
Teacher
Problems
Sequences / Series
Reasoning and Proof