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

lim_(n→+∞) ((((_1 ^n )(_2 ^n )...(_n ^n )))^(1/n) /(e^(n/2) ×n^(−(1/2)) ))=?

$$\underset{\mathrm{n}\rightarrow+\infty} {\mathrm{lim}}\frac{\sqrt[{\mathrm{n}}]{\left(_{\mathrm{1}} ^{\mathrm{n}} \right)\left(_{\mathrm{2}} ^{\mathrm{n}} \right)...\left(_{\mathrm{n}} ^{\mathrm{n}} \right)}}{\mathrm{e}^{\frac{\mathrm{n}}{\mathrm{2}}} ×\mathrm{n}^{−\frac{\mathrm{1}}{\mathrm{2}}} }=? \\ $$

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