Smells Like Something's Stirling

Calculus

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}