Real Analysis: Fibonnaci Numbers

phyxius117 · Feb 28, 2010

Homework Statement

Worksheet titled Fibonacci Worksheet defining F0 = F1 = 1 and Fn = Fn-2 + Fn-1 for n > 1, Fact 1 that the sequence is increasing and unbounded, Fact 2 that FnFn+2 = Fn+1 squared + (-1)^n, and Task 1 to prove 1 ≤ bn ≤ 2 for bn = Fn+1/Fn.

Homework Equations

In the image above

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!

Mathnerdmo · Feb 28, 2010

Try using fact 2 to find an equation involving the b_n terms.

Real Analysis: Fibonnaci Numbers

Homework Statement

Homework Equations

The Attempt at a Solution

Discussion

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