What is the Limit of the nth Root of a Fraction as n Approaches Infinity?

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Homework Statement



Show \lim\limits_{n\to\infty}\sqrt[n]{\frac{1}{n^2}}=1


Homework Equations





The Attempt at a Solution

No ideas
 
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I'd start by trying to find the limit of the log of that expression. l'Hopital's rule might come in handy.
 

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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