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Question Number 92767 by mathmax by abdo last updated on 09/May/20

let U_n =∫_0 ^1  e^(−nx) cosx dx  1) determine lim_(n→+∞) n^2  U_n   2)calculate Σ_(n=0) ^∞  U_n

$${let}\:{U}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:{e}^{−{nx}} {cosx}\:{dx} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{lim}_{{n}\rightarrow+\infty} {n}^{\mathrm{2}} \:{U}_{{n}} \\ $$$$\left.\mathrm{2}\right){calculate}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{U}_{{n}} \\ $$

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