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Question: let and bn be two convergent sequences of real...

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Let {α, and {bn} be two convergent sequences of real numbers with lim an -a and (a) Prove that if an S bn for every index n, then a < b. Hint: Consider the sequence [dn bn an, and use the fact that [0, oo) is closed (i.e. Lemma 2.21) b) Squeeze Theorem for sequences: Prove that if ab L and en) is a scquence satisfying bn for every index n, then scn is convergent and lm cn-L an Sn

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