*? Let (sn) be a sequence that converges. (a) Show that if sn > a for all but finitely many n, then lim sn > a. (b) Show that if sn

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Q: Let (an) be an unbounded sequence. Show that it has a subsequence (bk) = (ank) 1 such that lim = =…

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Q: advanced MATH   Suppose that the sn satisfies both limn→∞ s2n = 3 and limn→∞ s2n+1 = 3. (That is,…

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Q: 1 2 + xn (a) Prove by induction that în > 0 for all n € N. (b) Prove that (n) is a contractive…

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Q: Assume that the sequence shown below converges and find its limit. √3, √3+√3,√√3+√3+√3 √3+₁ " 3 +…

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Q: (ii) If (sn) is an unbounded decreasing sequence, then lim så -∞

A: Given that {sn} is an unbounded decreasing sequence. To show :- limn→∞sn=-∞

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Q: (c) Let (sn) be a sequence of negative numbers (sn <0 for all n E N). Prove that lim 8, = -00 if and…

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A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three sub…

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Q: 2. Let the sequence (n) be recursively defined by x1 = √√2 and xn+1 = √2+xn, n≥1. Show that (xn)…

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