Question Number 116250 by mathmax by abdo last updated on 02/Oct/20
![1)explicite U_n =∫_0 ^∞ e^(−n[x]) cos(3[x])dx 2) calculate lim_(n→+∞) U_n 3)find nsture of Σ U_n](https://www.tinkutara.com/question/Q116250.png)
$$\left.\mathrm{1}\right)\mathrm{explicite}\:\mathrm{U}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\infty} \:\mathrm{e}^{−\mathrm{n}\left[\mathrm{x}\right]} \mathrm{cos}\left(\mathrm{3}\left[\mathrm{x}\right]\right)\mathrm{dx} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{calculate}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\mathrm{U}_{\mathrm{n}} \\ $$$$\left.\mathrm{3}\right)\mathrm{find}\:\mathrm{nsture}\:\mathrm{of}\:\Sigma\:\mathrm{U}_{\mathrm{n}} \\ $$