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Unformatted text preview: LOGIC AND PROOF HOMEWORK 5 1. Prove by induction that 1 + 2 + 3 + … + n = n(n+1)/2 for every natural number n. 2. Prove by induction that 20 + 21 + 22 + … + 2n = 2n+1 – 1 for every natural number n. 3. Prove by induction that 3 divides n3 – n for every natural number n. 4. 2.4.7 (part h) 5. Prove by strong induction that every natural number greater than 1 is prime or a product of primes. 6. Prove by strong induction that each term Fn in the Fibonacci sequence is less than 2n. [Note: The sequence Fn of Fibonacci numbers {0, 1, 1, 2, 3, 5, 8, 13, …} is defined by the recurrence relation Fn = Fn‐1 + Fn‐2, with initial values F0 = 0 and F1 = 1.] 7. 2.5.3 (part a) 8. 2.5.3 (part b) ...
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 Spring '08
 EVINSON
 Calculus, Logic

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