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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.
 Spring '09

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