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Unformatted text preview: F n = 1 5 " 1 + 5 2 ! n 1 5 2 ! n # , n . n X k =1 F 2 k = F n F n +1 F 1 F 2 + F 2 F 3 + + F 2 n1 F 2 n = F 2 2 n 1 T. Yolcu, School of Mathematics at Georgia Tech. Email: tyolcu@math.gatech.edu . 1 6. Let f ( x ) = x 21 . Dene f n ( x ) = f ( f ( ( f ( f  {z } n times ( x ))) )) , n 1 . Namely, f n +1 = f ( f n ( x )) = f n ( f ( x )) for n 1 . Use the Principle of Mathematical Induction to show that (a) f n ( x ) = a, where a <1 , has no solution. (b) f n ( x ) = a, where a > , has only two distinct solutions. Hint: Use f n +1 ( x ) = f ( f n ( x )) = f 2 n1 and part (a). (c) f n ( x ) = a, where a = 0 , has n + 1 distinct solutions. Hint: Use f n +1 ( x ) = f 2 ( f n1 ( x )) = f 2 n1 ( f 2 n12) and part (b). 2...
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This note was uploaded on 05/12/2010 for the course MATH 2602 taught by Professor Costello during the Spring '09 term at Georgia Institute of Technology.
 Spring '09
 COSTELLO
 Math, Addition, Mathematical Induction

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