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Question Number 185383 by aba last updated on 20/Jan/23

$$\underset{\mathrm{n}\to +\mathrm{\infty }}{\lim }\frac{\sqrt[\mathrm{n}]{\left({}_1^{\mathrm{n}}\right)\left({}_2^{\mathrm{n}}\right)...\left({}_{\mathrm{n}}^{\mathrm{n}}\right)}}{{\mathrm{e}}^{\frac{\mathrm{n}}{2}}\times {\mathrm{n}}^{-\frac{1}{2}}}=?$$

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