# Power series

Contents
Power series are infinite series of the form Σaₙxⁿ (where n is a positive integer). Even though this family of series has a surprisingly simple behavior, it can be used to approximate very elaborate functions.
10 exercises available

### Power series intro

Power series is a sum of terms of the general form aₙ(x-a)ⁿ. As you can see, it's actually a function whose sum depends on the x-value. It is a generalization of geometric series, and an extremely useful class of series. Learn more about it in this tutorial.

### Taylor & Maclaurin polynomials intro

Taylor polynomials are a very clever way of approximating any function with a polynomial. Maclaurin polynomials are a special class of Taylor polynomials. Learn how these polynomials work in this tutorial.

### Maclaurin series of sin(x), cos(x), and eˣ

A Maclaurin series is essentially a Maclaurin polynomial with infinite terms. It turns out that the Maclaurin series of sin(x), cos(x), and eˣ return the exact same values as the functions themselves, for any x-value. Wow! Introduce yourselves to these special series and discover one of the most fascinating areas of all of mathematics!

### Power series function representation

We already saw how Taylor and Maclaurin series can be used to represent a variety of functions. In this tutorial, we will expand the scope of functions that we can represent with power series, by enriching our toolkit!

### Challenge series exercises

Review you knowledge about series with some challenging exercises.