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Question Number 84859 by M±th+et£s last updated on 16/Mar/20

show that  lim_(n→∞) ∫_0 ^1 ...∫_0 ^1 (n/(x_1 +x_2 +x_3 +...+x_n ))dx_1 dx_2 ...dx_n =2

$${show}\:{that} \\ $$$$\underset{{n}\rightarrow\infty} {{lim}}\int_{\mathrm{0}} ^{\mathrm{1}} ...\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{n}}{{x}_{\mathrm{1}} +{x}_{\mathrm{2}} +{x}_{\mathrm{3}} +...+{x}_{{n}} }{dx}_{\mathrm{1}} {dx}_{\mathrm{2}} ...{dx}_{{n}} =\mathrm{2}\: \\ $$

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