Smells Like Something's Stirling

Calculus Level 2

What is the value of the following limit?

\[ \lim_{n\to\infty} \dfrac{ \sqrt[n]{1 \times 2 \times \cdots \times n} }n \]

\[0\] \[\frac{1}{\pi}\] \[\frac{1}{e}\] \[\frac{4}{9}\] \[\frac{1}{2}\] \[1-\ln{2}\] \[\frac{\zeta{(3)}}{4}\] \[1-\frac{1}{\zeta{(2)}}=1-\frac{6}{{\pi}^2}\]

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