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

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 i=

.

n+1

n+1 |

2 |

n

th

(n+1)

n

n

∑

i=1

n+1 |

2 |