Ohhh, I’m forgetting that (-1)^n is x = 4
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Aha! That makes sense, by saying x=3 converges we’re making an assurance on that boundary, doesn’t help the other one.
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and thus R doesn’t _need_ to be _greater than_ 2. thanks so much!!

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Correct. This might seem silly in the real-valued case, but in complex analysis the radius of convergence is a circle.
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ohh, I realized another nuance while typing out my own answer to cement my understanding http://math.stackexchange.com/a/2124819/412218 …
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