# Dividing Polynomials 1/(1-x)? 1+x+x^2+x^3+... ______ 1-x | 1 1-x ______ x x-x^2 ________ x^2 x^2-x^3 ____ x^3 ... Therefore 1/(1-x) = 1+x+x^2+x^3+... For 1/(1-x)^2, 1/(1-x)^2 = 1/(1-2x+x^2) = 1+2x+3x^2+... so that (1+x+x^2+...)(1+x+x^2+...) = 1+2x+3x^2+... and (1-x)(1+2x+3x^2+...) = 1+x+x^2+... By dividing, you can get the Laurent series of any p(x)/q(x). Since [Integers] ~ [Polynomials], you can understand this as [Rational numbers] ~ [Rational functions], and [Infinite decimals] = [Real numbers] ~ [Infinite series].