10.7

Question 1

What is the general form of a power series?

Answer 1

∑cn(x-a)^n where:

a is the center of the series
cn are the coefficients

Question 2

What is the radius of convergence of a power series and how do you determine it?

Answer 2

The radius of convergence is the radius around a for which values of x converge

You can use a ratio test to find the radius of convergence.

After finding R, we test the end points x=a-r and x=a+r separately to determine if they are included in the interval of convergence