Real Analysis: Fibonnaci Numbers

phyxius117
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Homework Statement


task1.jpg



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

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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