Convergence of a Sequence: How to Determine and Find the Limit?

zelmac
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Homework Statement


Check whether the sequence a_{1}=\alpha ,\alpha > 0, a_{n+1}=6*\frac{a_{n}+1}{a_{n}+7} converges and find its limit if it does, depending on α.


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The Attempt at a Solution


I showed boundedness([0,6]) and found that in the case of convergence the limit is 2, but I don't know how to check its convergence... Any help is appreciated :)
 
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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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