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Unformatted text preview: : Base case. For n = 1 , Fib (1) = 1 < 5 3 . For n = 2 , Fib (2) = 1 < ( 5 3 ) 2 . Thus, the formula is correct for the base case. Induction Hypothesis. For all positive integers i < n , Fib ( i ) < ( 5 3 ) i . Induction Step. Fib ( n ) = Fib ( n 1) + Fib ( n 2) and, by the Induction Hypothesis, Fib ( n 1) < ( 5 3 ) n 1 and Fib ( n 2) < ( 5 3 ) n 2 . So, Fib ( n ) < ( 5 3 ) n 1 + ( 5 3 ) n 2 < 5 3 ( 5 3 ) n 2 + ( 5 3 ) n 2...
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This note was uploaded on 12/27/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.
 Fall '08
 BELL,D

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