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.
Students will be able to
Q1:
Let us consider 𝑔(𝑥)=𝑥3−𝑥.
Find a power series representation for 𝑔(𝑥).
Find its radius of convergence.
Q2:
Let us consider 𝑓(𝑥)=11+𝑥.
Find a power series representation for 𝑓(𝑥).
Find its interval of convergence.
Q3:
Consider ℎ(𝑥)=4𝑥1+𝑥.
Find a power series representation for ℎ(𝑥).
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