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Unformatted text preview: Practice Exam 2 11/7/06 Name: No calculators allowed. Show all work. DO NOT BEGIN TEST UNTIL INSTRUCTED TO DO SO. Write out and sign the Georgia Tech Honor Challenge below. I commit to uphold the ideals of honor and integrity by refusing to betray the trust bestowed upon me as a member of the Georgia Tech community. 1 2 (1) (a) How many nonnegative integer solutions are there to 2 x 2 y 2 z = 512? The solutions to 2 x 2 y 2 z = 512 are exactly the solu tions to x + y + z = 9. The solutions for which x , y , and z are nonnegative integers may be counted by considering the number of ways to put 9 unlabeled balls into 3 labeled urns. This is equivalent to the number of ways of putting 2(= 3 1) dividers into 11(= 9 + 3 1) slots; that is: parenleftbigg 11 2 parenrightbigg (b) How many positive integer solutions are there to 2 x 2 y 2 z = 512? The solutions to x + y + z = 9 are exactly the solutions to ( x 1) + ( y 1) + ( z 1) + 3 = 9 ( x 1) + ( y 1) + ( z 1) = 6 Since x being a positive integer means ( x 1) is non negative, we count the number of ways of putting 2(= 3 1) dividers into 8(= 6 + 3 1) slots. That is: parenleftbigg 8 2 parenrightbigg (2) (a) Give both the power series and the closed form of the generating func tion for the following sequence: { a k } ∞ k =0 = { 1 , , , 1 , , , 1 , , , 1 , , , 1 , , , 1...
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This note was uploaded on 05/12/2010 for the course MATH 2602 taught by Professor Costello during the Fall '09 term at Georgia Tech.
 Fall '09
 COSTELLO
 Math

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