CMSC 250 Jerry Alan Fails Due Tuesday July 3 2007 HW 8 Student ID You must work alone on your homework and homework must be written legibly single sided on your own lined paper or typed with the answers clearly labeled and in the sequential order as assigned You must write your name and university ID number in the upper right hand corner of your homework Staple all pages together and be sure that your name appears on every sheet 1 10 points if wrong Write your name clearly on each page Write the time and place of Exam 2 2 10 points Suppose P n is a property such that i P 0 ii For all integers k 0 if P k is true then P 3k is true Must it follow that P n is true for all integers n 0 If yes explain why if no give a counterexample 3 70 points For each of the following say whether it is true or false If true use mathematical induction to prove it If false give a specific counterexample a n 1 8 32 n 1 n b n i i 1 1 n 1 i 1 i 2 2 n 2 i 1 c n 2 4 3n 1 n d n k 3n k 1 2 k 2 e n 6 1 n2 2n 5 2 f m n m n 3 2 n 4 20 points Suppose a4 a5 a6 a7 is a sequence defined as follows a1 0 a2 1 a3 2 ak ak 1 ak 2 ak 3 for all integers k 4 a 5 points What are a4 a5 a6 a7 b 5 points What can you say about the parity i e evenness and oddness of ak in general c 10 points Prove it HW 8 Due Tuesday July 3 2007 Page 1 of 2 CMSC 250 Jerry Alan Fails Due Tuesday July 3 2007 HW 8 Student ID 5 No points will be awarded for this assignment unless this is done Sign your name to the following honor code statement I pledge on my honor that I have not given or received any unauthorized assistance on this assignment HW 8 Due Tuesday July 3 2007 Page 2 of 2
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