Real Analysis: Fibonnaci Numbers

[phyxius117]

Homework Statement

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]

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