An Iterative Process Applied to Equilateral Triangles Resulting to the Identity 1/3+1/9+1/27+…=1/2.

Abstract

In this paper, we define a particular iterative process and apply it to triangles. It was shown that the process results to self-similar triangles if and only if the generator triangle is an equilateral triangle. Furthermore, the identity 1/3+1/9+1/27+...=1/2 resulted from the process.