Summing a series on an interval of convergence

1. May 4, 2010

c.dube

1. The problem statement, all variables and given/known data
Find the interval of convergence of the series and, within this interval, the sum of the series as a function of x.
$$\sum^{\infty}_{n=0}\frac{(x-1)^{2n}}{4^n}$$
2. Relevant equations
N/A
3. The attempt at a solution
Finding the interval is easy, using the ratio test it reduces down to
$$|\frac{(x-1)^{2}}{4}|<1$$
$$-1<x<3$$

However, I have no idea how to do the second part. Any help?

Last edited: May 4, 2010
2. May 4, 2010

System

1- You should check the end points to decide the interval.
2- For the sum, I think you know something called "geomtric series", right?

3. May 4, 2010

Duh! Thanks.