Power series allow us to represent associated functions on an appropriate interval. Represent a function as a Taylor series or a Maclaurin series. A Taylor polynomial for f (x) is a partial sum of the Taylor series for f (x). Interpret Taylor series and Maclaurin series. The Maclaurin series for 1/(1-x) a geometric series. The Maclaurin series for sin x, cos x, and e^x provides the foundation for constructing the Maclaurin series for other functions.