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Uniform Convergence of Sequnece

Prove : Let f1,f2.... be a sequence of continuous functions convergent uniformly on a bounded closed interval [a,b] and let c E[a,b] . For n = 1,2,...., define .....
Then the sequence g1,g2.... converges uniformly on [a,b].

Is the same true if [a,b] is replaced by ?

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Solution Summary

Uniform Convergence of Sequnece is investigated. The solution is detailed and well presented.