Lesson: Representing Rational Functions Using Power Series Mathematics • 12th Grade

In this lesson, we will learn how to use the formula of the infinite sum of geometric series to find a power series representation for some rational functions.

Lesson Plan

Students will be able to

algebraically manipulate certain rational functions into a form that can be expressed as a power series, and vice versa,
find the radius of convergence of the resulting series.

Lesson Video

Lesson Worksheet

Q1:

Let us consider .

Find a power series representation for .

Find its radius of convergence.

Q2:

Let us consider .

Find a power series representation for .

Find its interval of convergence.

Q3:

Consider .

Find a power series representation for .

Find its interval of convergence.