The radius of convergence for the power series (x-3)^2n/n from n=1 to infinity is equal to 1. what is the interval of convergence?

The solution to the problem is as follows:

|x−3|<1
X−3<1
and
−(x−3)<1
first one
X−3<1⇒x<1+3=4
for the second
−(x−3)<1⇒x−3>−1⇒x>3−1=2
thus
2<x<4

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