Converging to Infinity: Solving the Limit of n!²/(2n)!

bluedevilgirl
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Homework Statement



Find the limit of the given sequence as n -> inf.

((n!)^2)/(2n)!


Homework Equations



We have been told that the squeeze theorem may be helpful.


The Attempt at a Solution



Using the squeeze theorem, I get stuck. I tried factoring some things out, and seem to be extremely stuck.
 
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Try the ratio test; I'm quite sure I did this sum that way once.
 

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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