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Unformatted text preview: Rob Bayer Math 55 MT2 Review July 24, 2009 Instructions Work through the following review problems as a group Make sure to focus not just on getting the correct answers, but also on how you would actually write your proofs/solutions Feel free to skip aroundtheres way more problems here than the actual midterm will have, so focus on whatever your group wants practice with. As always with review/practice tests, the inclusion or exclusion of certain topics should not be taken as an indication of what will be on the actual midterm. Induction and Recursion 1. Prove that 1 + 1 4 + 1 9 + + 1 n 2 < 2- 1 n for all positive n . 2. Consider the set of bit strings defined as followed: 1 S If w,v S , then w S , and w 1 v S . 3. Use induction to prove that n 2 + 3 n is always even. (Can you think of a much easier proof?) Show that every string in S contains an odd number of 1 s 4. Find all solutions to the recurrence relation a n =- 2 a n- 1 + 15 a...
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- Summer '08