Unformatted text preview: 2. Problem 8 Page 288. Do each part in no more than 10 lines. 3. Problem 9 Page 288. Do each part in no more than 10 lines. 4. Problem 13 Page 288. Do this in no more than 30 lines. You are given that a n → L . Name a subsequence b k = a n k . You want to prove that b k → L . Useful is the fact that k ≤ n k for all k . 5. Problem 18 Page 288. Do this in no more than 20 lines. Use induction. 6. Problem 19 Page 289. Do this in no more than 1 page. Use induction to prove that x n > √ 3 for all n ≥ 2. Then prove that x n +1-x n < 0. Thus h x n i n ≥ 2 is decreasing and bounded below, hence has a limit, say α . Show that 2 α = α + 3 /α . Use this to show that α = √ 3....
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This note was uploaded on 10/15/2011 for the course MATH 23b taught by Professor Bonglian during the Spring '09 term at Brandeis.
- Spring '09