145HW4 - Hint: consider the property “every integer...

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Homework assignment Number 4 Math 145 // due on 02/02/2007 1. Problems Section 4.3: 5, 6, 8, 9, 11, 13, 15. 2. Let b n be a sequence of numbers such that b o = 0, b 1 = 1 and satisfying the recurrence b n +1 = 2 b n + 5 b n - 1 . Find the value of b n . 3. Show that c n = 1 17 h‡ 3+ 17 2 · n - 3 - 17 2 · n i is an integer for any n . 4. Show by induction that every integer can be written as the sum of distinct Fibonacci numbers.
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Unformatted text preview: Hint: consider the property “every integer smaller than F n can be written as a sum of distinct Fibonacci numbers”. Extra question: consider uniqueness of such a decomposition. 1...
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This homework help was uploaded on 04/08/2008 for the course MATH 145 taught by Professor Peche during the Spring '07 term at UC Davis.

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