A Graph Theory Interpretation of the Sum of the First n Integers

A complete graph on vertices has edges. This number is also the sum of the first integers, as shown here: the complete graphs are built up by adding one vertex at a time, and the colors show that the vertex adds edges, thus showing visually that .


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This Demonstration was suggested by the following article:
J. DeMaio and J. Tyson, "Proof without Words: A Graph Theoretic Summation of the First Integers," The College Mathematics Journal, 38, 2007 p. 296.
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Related Curriculum Standards

US Common Core State Standards, Mathematics