homework5 - LOGIC AND PROOF HOMEWORK 5 1 Prove by induction...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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) ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online