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Question Number 142980 by mathmax by abdo last updated on 08/Jun/21

$$\mathrm{find}{\mathrm{U}}_{\mathrm{n}}={\int }_0^{\mathrm{\infty }}{\mathrm{e}}^{-{\mathrm{nx}}^2}\log (2+{\mathrm{e}}^{\mathrm{x}})\mathrm{dx}(\mathrm{n}⩾1)$$$$\mathrm{determine}\mathrm{nature}\mathrm{of}\mathrm{\Sigma }{\mathrm{U}}_{\mathrm{n}}\mathrm{and}\mathrm{\Sigma }{\mathrm{nU}}_{\mathrm{n}}$$

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