Question Number 185383 by aba last updated on 20/Jan/23
$$\underset{\mathrm{n}\rightarrow+\infty} {\mathrm{lim}}\frac{\sqrt[{\mathrm{n}}]{\left(_{\mathrm{1}} ^{\mathrm{n}} \right)\left(_{\mathrm{2}} ^{\mathrm{n}} \right)…\left(_{\mathrm{n}} ^{\mathrm{n}} \right)}}{\mathrm{e}^{\frac{\mathrm{n}}{\mathrm{2}}} ×\mathrm{n}^{−\frac{\mathrm{1}}{\mathrm{2}}} }=? \\ $$