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Example of Uniformly Convergent Sequence of Functions and Weierstrass Test

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Find an example of a sequence of continuous functions on fn on [0,1] such that the series...converges uniformly on [0,1] but the series ... diverges. Is it a counterexample for the Weierstrass test?
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Find an example of a sequence of continuous functions on on [0,1] such that the series converges ...

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