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Abel's Theorem. Let f(x) = ∑ anxn be a power series with finite positive radius of convergence R. If the series converges at
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![SOLVED: Given an example of a sequence of functions { fn(x)} on (0,1) that converges point- wise to f(c) = 1 but does not converge uniformly [6] (ii) A power series Cn](https://cdn.numerade.com/ask_images/444a7eb445084a278c155fa488023177.jpg "SOLVED: Given an example of a sequence of functions { fn(x)} on (0,1) that converges point- wise to f(c) = 1 but does not converge uniformly [6] (ii) A power series Cn")
SOLVED: Given an example of a sequence of functions { fn(x)} on (0,1) that converges point- wise to f(c) = 1 but does not converge uniformly [6] (ii) A power series Cn
MathCS.org - Real Analysis: 8.2. Uniform Convergence
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Power series and continuity We fix (an), the series f(x) = ∑ akxk and the partial sums fn(x) = ∑ Definition 0.1. We say that
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