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 .
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.