Let`s say that $f(x)$ is represented by a power series, and the series is conditionally convergent at the endpoint $x=R+C$, so is $f(x)$ continuous at that point? is it differentiable? since we know that conditional convergence means that I can get any sum I want by rearranging the terms?
2026-03-27 19:52:52.1774641172
power series and conditional convergence at an end point
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Then $f$ is continuous at that point too; that's what Abel's theorem says. However, $f$ doesn't have to be differentiable at that point.
The fact that you can get any sum you want by rearranging the terms is not relevant here.