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Power series,convergence of sequences of functions, and uniform limits

The question is in attached file.

Suppose a sequence of continuous functions, { ?n }, has the property that ?n  ? and
&#61474;&#61541; > 0, &#61476; &#61540; > 0 such that if | x - y | < &#61540; then &#61474;n, | ?n (x) - ?n (y)| < &#61541; Prove that ? is
continuous.

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Solution Summary

This is a proof regarding a sequence of continuous functions.

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