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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 around–there’s 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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This note was uploaded on 09/10/2009 for the course MATH 55 taught by Professor Strain during the Summer '08 term at Berkeley.
- Summer '08