This document provides examples of representing functions as power series. It begins by expressing 1/(1-x) as a power series valid for |x|<1. It then uses this to find power series representations of other functions like 1/(1+x^2), 1/(x+2), and x^3/(x+2) by making substitutions. It also discusses differentiation and integration of power series according to specified rules. Examples find power series for 1/(1-x)^2, ln(1+x), and tan^-1(x) by these operations. All power series are found along with their intervals of convergence.