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1-calculate-u-n-0-e-nx-ln-1-x-dx-with-n-integr-natural-2-calculate-lim-n-u-n-3-find-n-0-u-n-




Question Number 47063 by maxmathsup by imad last updated on 04/Nov/18
1)calculate u_n = ∫_0 ^∞   e^(−nx) ln(1+x)dx  with n integr natural  2) calculate lim_(n→+∞) u_n   3) find Σ_(n=0) ^∞  u_n
$$\left.\mathrm{1}\right){calculate}\:{u}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{nx}} {ln}\left(\mathrm{1}+{x}\right){dx}\:\:{with}\:{n}\:{integr}\:{natural} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{lim}_{{n}\rightarrow+\infty} {u}_{{n}} \\ $$$$\left.\mathrm{3}\right)\:{find}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{u}_{{n}} \\ $$

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