Limit of the sequence $\lim_{n\rightarrow\infty}\sqrt[n]n$ 
Possible Duplicate:
$\lim_{n \to +\infty} n^{\frac{1}{n}} $ 

I know that 
$$\lim_{n\rightarrow\infty}\sqrt[n]n=1$$
and I can imagine that $n$ grows linearly while $n$th root compresses it exponentially and therefore the result is $1$, but how do I calculate it?

$$\lim_{n\rightarrow\infty}\sqrt[n]n$$
$$=\lim_{n\rightarrow\infty}e^{\frac{\ln(n)}{n}}$$
and as we know that $\lim_{n\rightarrow\infty}\frac{\ln(n)}{n} = 0$ {apply  l'Hospital's rule}
So $$\lim_{n\rightarrow\infty}\sqrt[n]n=1$$
