Power series,convergence of sequences of functions, and uniform limits
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The question is in attached file.
Suppose a sequence of continuous functions, { ?n }, has the property that ?n  ? and
 > 0,   > 0 such that if | x - y | <  then n, | ?n (x) - ?n (y)| <  Prove that ? is
continuous.
https://brainmass.com/math/real-analysis/power-series-convergence-sequences-functions-uniform-limits-15066
Solution Preview
Please see the attachment.
Suppose a sequence of continuous functions, { ƒn }, has the property that ƒn ƒ and
> 0, > 0 such that if | x - y | < then n, | ƒn (x) - ƒn (y)| < Prove that ƒ is
continuous.
Proof. In order to show that ƒ is ...
Solution Summary
This is a proof regarding a sequence of continuous functions.
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