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## Main Question or Discussion Point

Given a power series [itex]\sum a_n x^n[/itex] with radius of convergence [itex]R[/itex], it seems that the series converges uniformly on any compact set contained in the disc of radius [itex]R[/itex]. This might be a silly question, but what's an example of a power series that doesn't actually also converge uniformly on the whole open disc of radius [itex]R[/itex]? I am assuming uniform convergence on all compact subsets does not imply uniform convergence on the whole

*open*disc?