(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?

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# Summing a series on an interval of convergence

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