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lim-n-n-1-x-n-x-2-1-x-2-x-n-1-dx-n-1-2-




Question Number 161529 by qaz last updated on 19/Dec/21
lim_(n→∞) n((∫_1 ^(+∞) ((x^n −x^2 +1)/(x^2 (x^n +1)))dx)^n −(1/2))=?
$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}n}\left(\left(\int_{\mathrm{1}} ^{+\infty} \frac{\mathrm{x}^{\mathrm{n}} −\mathrm{x}^{\mathrm{2}} +\mathrm{1}}{\mathrm{x}^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{n}} +\mathrm{1}\right)}\mathrm{dx}\right)^{\mathrm{n}} −\frac{\mathrm{1}}{\mathrm{2}}\right)=? \\ $$

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