Question: Let fe C(R). Prove that the sequence {f} defined by n-1 k f(x + 2) n fn(x) = = n k=0 converges uniformly on

Let fe C(R). Prove that the sequence {f} defined by n-1 k f(x + 2) n fn(x) = = n k=0 converges uniformly on each finite interval [a, b]. As a byproduct, find its limit for each a.

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