h1 115A - simple formula for f 1 + f 3 + + f 2 n-1 . 4....

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MAT 115A University of California Fall 2010 Homework 1 due October 6, 2010 1. Rosen 1.1 #5, pg. 13 Use the well-ordering principle to show that 3 is irrational. 2. Rosen 1.3 #8, pg. 27 Use induction to prove that n k =1 k 3 = ± n ( n +1) 2 ² 2 . 3. Rosen 1.4 #7, pg. 33 Find and prove a simple formula for the sum of the first n Fibonacci numbers with odd indices when n is a positive integer. That is, find a
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Unformatted text preview: simple formula for f 1 + f 3 + + f 2 n-1 . 4. What is the value of [ x ] + [-x ] where x is a real number? 5. Rosen 1.5 #28, pg. 41 Show that if a is an integer, then 3 divides a 3-a . 6. Show that the n-th Fibonacci number f n is divisible by 4 if and only if n is divisible by 6. 1...
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This note was uploaded on 10/23/2010 for the course MATH math 115A taught by Professor Anne during the Spring '10 term at UC Davis.

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