Example 8.3.9 (a): Power Series Center
Find the center and radius of convergence for the power series (3x - 2)n
The 3 in front of the x is preventing us from reading off the center of the series. Thus, we'll 'take it out':
(3x - 2)n = (3 (x - 2/3))n = 3n (x - 2/3)n
Now it's easy to see that the center of convergence is c=2/3 and the radius is r=1/3.