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Please show all work necessary in order to receive a thumbs up. (Exercise 2.5.4) Assume (an) is a bounded sequence with the property that every

Please show all work necessary in order to receive a thumbs up.

(Exercise 2.5.4) Assume (an) is a bounded sequence with the property that every convergent subsequence of (an) converges to the same limit a e R. Show that (a, ) must converge to a

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