Proving Limit at Infinity: n^(1/n) = 1

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Homework Statement



How can I prove that:

\lim_{n \rightarrow \infty} n^{\frac{1}{n}}=1

Isn't \infty^{0} indeterminate?
Thanks!


Homework Equations





The Attempt at a Solution

 
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Yes, it is indeterminant. That's not the end of the story. Indeterminant just means you don't know what the limit is yet. Take the log. Can you prove (1/n)*log(n) approaches 0?
 
That becomes 0*\infty, isn't that indeterminate as well?
 
Can't you use L'Hopital's rule?
 
Right. Thanks guys!
 

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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