(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find theintervalof convergence of the series and, within this interval, the sum of the series as a function of x.

[tex]\sum^{\infty}_{n=0}\frac{(x-1)^{2n}}{4^n}[/tex]

2. Relevant equations

N/A

3. The attempt at a solution

Finding the interval is easy, using the ratio test it reduces down to

[tex]|\frac{(x-1)^{2}}{4}|<1[/tex]

[tex]-1<x<3[/tex]

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

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Summing a series on an interval of convergence

**Physics Forums | Science Articles, Homework Help, Discussion**