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Please provide all work necessary for the entire question in order to receive a thumbs up. Let a E O where O is an open

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Please provide all work necessary for the entire question in order to receive a thumbs up.

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Let a E O where O is an open subset of R. II (C,),, is a sequence converging to r, prove that all but a finite number of terms of (2,) , must be contained in O

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