# We willlookatsomeoftheconsequencesbelow

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Unformatted text preview: is in tabular form we get: Month 0 1 2 3 4 5 6 7 8 9 10 11 12 Adult Pairs Young Pairs Total This is one of the first examples of a recursive sequence since each term is the sum of the previous two. Indeed, if we let Fn denote the nth Fibonacci number, then F1 = F2 = 1, Fn = Fn‐2 + Fn‐1, n ≥ 3 This sequence – number A000045 in the Online Encyclopedia of Integer Sequences – has so many mathematical and scientific consequences that there is a journal devoted to it, Fibonacci Quarterly. We will look at some of the consequences below. Property 1: The sum of the first n Fibonacci numbers is Fn+2 – 1. Proof: Two other properties that we will not prove are the following: Property 2: F2n+1 = (Fn+1)2 + (Fn)2, n ≥ 1. Ex. Ex. Property 3: , n ≥ 1 Ex. Ex....
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## This note was uploaded on 09/22/2011 for the course MAC 2311 taught by Professor Evinson during the Spring '08 term at University of Central Florida.

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