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Define the fibonacci numbers by f(0) = 0; f(1) = 1; and then recursively for natural numbers n ≥ 2 by f(n) = f(n-1) + f(n-2). a) Write out the first 7 fibonacci numbers. I b) Make a conjecture about which numbers n will give us that f(n) will be an even number. c) Prove an exact characterization of these numbers using strong induction. (i.e. show that if your characterization is true up to some point, then it would be true just after that)

Define the fibonacci numbers by f(0) = 0; f(1) = 1; and then recursively for natural numbers n ≥ 2 by f(n) = f(n-1) + f(n-2). a) Write out the first 7 fibonacci numbers. I b) Make a conjecture about which numbers n will give us that f(n) will be an even number. c) Prove an exact characterization of these numbers using strong induction. (i.e. show that if your characterization is true up to some point, then it would be true just after that)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Define the fibonacci numbers by f(0) = 0; f(1) = 1; and then recursively for natural numbers n ≥ 2 by f(n) = f(n-1) + f(n-2). a) Write out the first 7 fibonacci numbers. I b) Make a conjecture about which numbers n will give us that f(n) will be an even number. c) Prove an exact characterization of these numbers using strong induction. (i.e. show that if your characterization is true up to some point, then it would be true just after that)
Transcribed Image Text:Define the fibonacci numbers by f(0) = 0; f(1) = 1; and then recursively for natural numbers n ≥ 2 by f(n) = f(n-1) + f(n-2). a) Write out the first 7 fibonacci numbers. I b) Make a conjecture about which numbers n will give us that f(n) will be an even number. c) Prove an exact characterization of these numbers using strong induction. (i.e. show that if your characterization is true up to some point, then it would be true just after that)
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