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Question Number 116250 by mathmax by abdo last updated on 02/Oct/20

$$1)\mathrm{explicite}{\mathrm{U}}_{\mathrm{n}}={\int }_0^{\mathrm{\infty }}{\mathrm{e}}^{-\mathrm{n}\left[\mathrm{x}\right]}\cos \left(3\left[\mathrm{x}\right]\right)\mathrm{dx}$$$$2)\mathrm{calculate}{\lim }_{\mathrm{n}\to +\mathrm{\infty }}{\mathrm{U}}_{\mathrm{n}}$$$$3)\mathrm{find}\mathrm{nsture}\mathrm{of}\mathrm{\Sigma }{\mathrm{U}}_{\mathrm{n}}$$

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