Please prove: $ \lim_{n\to \infty}\sqrt[n]{\frac{1}{n!}} = 0 $ Possible Duplicate:
  $ \lim\limits_{n \to{+}\infty}{\sqrt[n]{n!}}$ is infinite  




Please prove:
$$
\lim_{n\to \infty}\sqrt[n]{\frac{1}{n!}} = 0
$$
Hint: When writing out $n!$, you have 
\[ n! = n \cdot (n-1) \cdots \left\lceil \frac n2\right\rceil \cdots 1 \]
so at least $\lfloor \frac n2\rfloor$ of the factors are larger then $\lceil \frac n2\rceil$.
So $n! \ge \lceil \frac n2\rceil^{\lfloor \frac n2\rfloor}$.
Just try to put n equal to infinity. since 'n' appears in the denominator it will tend to zero. 

Please confirm the answer.