Computing the $\lim_{n\to\infty} n^{\frac{1}{n!}}$? I want to find the following limit
$$\lim\limits_{n\rightarrow \infty} n^{\frac{1}{n!}}$$ 
I tried solution as follows:
Let $L=n^{\frac{1}{n!}}$ this implies $\log L=\frac{\log n}{n!}$ which is $\frac{\infty}{\infty}$ form as $n\rightarrow \infty.$ Don't know how to proceed. Help required

Hint:
$$1 \le n^{1/n!} \le (n!)^{1/n!}$$
