Taylor Series for $\frac{1}{1+x^2}$ at $x=a$

Abstract

We determine a formula for all coefficients of the Taylor series for the function $ \frac{1}{1+x^2} $ centered at $ x=a $ for any real number $ a $ along with the radius of convergence of the series. We utilize complex numbers to extend a standard calculus technique involving geometric series, but we write the coefficients using real numbers only.