Real Analysis: Fibonnaci Numbers

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SUMMARY

The discussion focuses on proving properties of the Fibonacci sequence, specifically the bounds of the sequence defined by the terms bn. The main goal is to demonstrate that the supremum of bn is 2 and the infimum is 1, establishing that the sequence remains within the interval [1, 2] for all n. The participants suggest utilizing established mathematical facts to derive an equation involving the bn terms to support this proof.

PREREQUISITES
  • Understanding of Fibonacci sequence properties
  • Knowledge of supremum and infimum concepts
  • Familiarity with real analysis proofs
  • Ability to manipulate sequences and series
NEXT STEPS
  • Study the properties of the Fibonacci sequence in detail
  • Learn about supremum and infimum in real analysis
  • Explore techniques for proving bounds of sequences
  • Review examples of real analysis proofs involving sequences
USEFUL FOR

Students of real analysis, mathematicians interested in sequence behavior, and anyone studying the properties of Fibonacci numbers.

phyxius117
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Homework Statement


task1.jpg



Homework Equations


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The Attempt at a Solution


Well it's a proof. I am thinking about doing it directly. Somehow showing that sup of bn is 2 and inf of bn is 1 and therefore the sequence must be between 1 and 2 for all n. But I am not sure, please help!
 
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Try using fact 2 to find an equation involving the bn terms.
 

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