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# hw03 - CS 70 Spring 2005 Discrete Mathematics for CS...

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Discrete Mathematics for CS Spring 2005 Clancy/Wagner HW 3 Due Thursday, February 10 Coverage: This assignment involves topics from the February 1 and 3 lectures and from sections 3.4 through 3.6 of Rosen. Administrative reminders: We will accept only unformatted text files or PDF files for homework sub- mission. Include your name, login name, section number, and partner list in your submission. Give the command submit hw3 to submit your answers to this assignment. Homework exercises: 1. (14 pts.) Fibonacci numbers The Fibonacci numbers are defined as follows: F 0 = 0 F 1 = 1 F n = F n - 2 + F n - 1 for n > 1 (a) List the first ten Fibonacci numbers ( F 0 through F 9 ). (b) Consider the following Scheme procedure that, given n, returns F n . (define (fib n) (cond ((= n 0) 0) ((= n 1) 1) (else (+ (fib (- n 1)) (fib (- n 2)))) ) ) Let T n be the number of addition operations required in the computation of (fib n) . List the values T 0 through T 9 . (c) State and prove a relationship between the T numbers and the F numbers. (d) Prove that F n + 1 F n - 1 - F 2 n = ( - 1 ) n . CS 70, Spring 2005, HW 3

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hw03 - CS 70 Spring 2005 Discrete Mathematics for CS...

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