Proof: Xn<N!: A Mathematical Exploration

dannysaf
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proof xn < n!
 
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We would be happy to help you if you at least try the problem yourself and show us what you have tried
 
Obviously not.

31>1!

Have you started trying to prove it yet? Presumably the question asks to prove that for large enough n... what are your initial thoughts?
 
Maybe he means n^n<n! becuase there is always x=n!^{1\over n} ?

If so, you need to construct your argument around n^n = n*n*n*n...*n (n times) and n! = n(n-1)(n-2)...3.2.1 I think.
 
Perhaps for n approaching infinity?
 

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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