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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 Fall '08
 BELL,D
 Mathematical Induction, Natural number, base case, fib

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