hw4fa02 - where the induction hypothesis is applied in each...

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COT3100C-01, Fall 2002 Assigned: 10/17/2002 S. Lang Assignment #4 (40 pts.) Due: 10/24 in class by 8:45 am Instructions: Write your answer neatly and concisely. Show all your work and steps involved in simplification and manipulation of algebra expressions. In particular, mark clearly when and where the induction hypothesis is applied in induction proofs. Answer keys from assignments given in previous semesters (e.g. http://www.cs.ucf.edu/courses/cot3100.fall00/section1/homework/key5fa00.doc , and http://www.cs.ucf.edu/courses/cot3100.spr2000/section1/homework/key5sp00.doc ) can be consulted for proper writing style. Illegible scribbles or missing steps will result in minimum credit . Use induction to prove each of the following questions, and be sure to mark clearly when and
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Unformatted text preview: where the induction hypothesis is applied in each question: 1. (10 pts.) . 16 5 ) 1 4 ( 5 5 , 1 integer for that Prove 1 1 +-= + = n j n n n j j 2. ).) , ( ) 1 , 1 ( ) , 1 ( identity Triangle s Pascal' the Recall : (Hint constant positive arbitrary an is where ), , 1 ( ) , ( , integer for that Prove pts.) (10 k r C k r C k r C r n n r C j j r C n n j =--+-+ + = + = 3. (10 pts.) Prove that 421 | (20 n +2 + 21 2 n +1 ) for all integer n 0. 4. (10 pts.) Suppose a sequence a , a 1 , , a n , is defined by the following recurrence: a = 6, a 1 = 13, and 2 1 6--+ = n n n a a a , for n 2. Prove that the sequence a n satisfies the formula a n = 5 (3) n + (2) n for all integer n 0....
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This document was uploaded on 07/14/2011.

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