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Homework # 6 (Chapter 4) (20 points, Due on Wednesday, October 26) Question 1. [3 points each] Use the Monotone Convergence Theorem to prove that each of the following sequences is convergent and then find the limit of each sequence. (A) 3 1 s and 17 10 1 n n s s for 1 n . (B) 5 1 s and 7 2 1 1 s s n for 1 n . Question 2. [2 points each] Determine whether the given limits exist and find their values. Give clear explanation. (A) 1 2 7 5 lim n n n (B) ) ( lim 2 n n n n (C) 2 ) 1 1 ( lim n n n Question 3. [2 points each] Prove or disprove 1. Every monotone sequence is convergent. 2. Every Cauchy sequence is monotone. 3. Every Cauchy sequence is bounded. 4. Every sequence has a convergent subsequence.
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Subject: Math

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