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HW4 - 5 Problem 3.26 Page 73 Give an induction proof where...

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Math 23b Homework 4 Spring, 2009 Due Wednesday, March 4. Be sure to write clearly, using complete sentences. Do not use abbreviations like s.t., w/, w/o, b/c, c/o, etc. In all problems you must prove that your answer is correct, even if the problem does not explicitly ask you to do so. 1. Problem 3.2 Page 71. Hint: What is a statement that should be true for all n ? 2. Problem 3.17 Page 72. 3. Problem 3.22 Page 72. Note that a 1 , .., a n R . You should use the Triangle Inequality in your inductive step. 4. Problem 3.23 Page 72.
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Unformatted text preview: 5. Problem 3.26 Page 73. Give an induction proof, where P ( n ) is the statement that a n = n 3-n + 1. 6. Problem 3.30 Page 73. Do this without using induction. Use two results we have proved in class. 7. Problem 3.57 Page 75. The word sequence means list. There is a typo: replace “ n ≥ 2” by “ n ≥ 3.” In the inductive step, assume 1 ≤ a n-2 ≤ 2 and 1 ≤ a n-1 ≤ 2, and prove that the formula for a n gives a number between 1 and 2....
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