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.
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 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.
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!
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!