Recursion is a familiar topic in the study of numerical analysis and dynamical systems. Fixed point iteration is the basic iteration method in numerical analysis and is employed to study esoteric topics such as chaos. This article describes a familiar application of the summing of a geometric series. Graphical analysis clearly portrays the monotone and spiraling cases of a convergence. Explorations of divergent series are also given. These investigations give an understandable beginning for the study of fixed point iteration, dynamical systems and chaos.