hw5fa00 - n 1. ( Hint : Use n = 1 in the Basis step. Assume...

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COT3100.01, Fall 2000 Assigned: 11/09/2000 S. Lang Assignment #5 (40 pts.) Due: 11/21 in class Use induction to prove each of the following statements: 3. Define a function g ( n ) for n 0 by the following recurrence: g (0) = 1; g (1) = 14; and g ( n ) = 3 g ( n - 1) + 4 g ( n - 2), for n 2. Then g ( n ) = 3(4 n ) - 2( - 1) n , for n 0. 4. The expression n 2 - 1 is divisible by 8 for all odd integer
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Unformatted text preview: n 1. ( Hint : Use n = 1 in the Basis step. Assume n = k for some odd integer k in the Induction Hypothesis step; then use n = k + 2 in the Induction step.) . 2 for , ) 1 ( 2 1 2 4 3 1 1 1. 2 2 + +-= -= n n n n i n i . 1 for , 2 1 2 3 1 2. 2 1 3 - = n n i n i...
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