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lim-n-0-1-i-1-n-j-1-n-x-j-n-2-x-i-n-2-dx-




Question Number 160427 by qaz last updated on 29/Nov/21
lim_(n→∞) ∫_0 ^1 Σ_(i=1) ^n ((Π_(j=1) ^n (x+(j/n^2 )))/(x+(i/n^2 )))dx=?
$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\int_{\mathrm{0}} ^{\mathrm{1}} \underset{\mathrm{i}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\underset{\mathrm{j}=\mathrm{1}} {\overset{\mathrm{n}} {\prod}}\left(\mathrm{x}+\frac{\mathrm{j}}{\mathrm{n}^{\mathrm{2}} }\right)}{\mathrm{x}+\frac{\mathrm{i}}{\mathrm{n}^{\mathrm{2}} }}\mathrm{dx}=? \\ $$
Answered by Kamel last updated on 30/Nov/21
=(√e)
$$=\sqrt{{e}} \\ $$

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