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let-u-k-pi-2-kpi-pi-2-k-1-pi-e-t-cost-dt-1-calculate-u-k-2-let-A-n-k-0-n-u-k-find-lim-n-A-n-




Question Number 42797 by maxmathsup by imad last updated on 02/Sep/18
let u_k = ∫_(−(π/2) +kπ) ^(−(π/2) +(k+1)π)   e^(−t)  cost dt  1) calculate u_k   2) let A_n =Σ_(k=0) ^n  u_k      find lim_(n→+∞)  A_n
$${let}\:{u}_{{k}} =\:\int_{−\frac{\pi}{\mathrm{2}}\:+{k}\pi} ^{−\frac{\pi}{\mathrm{2}}\:+\left({k}+\mathrm{1}\right)\pi} \:\:{e}^{−{t}} \:{cost}\:{dt} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{u}_{{k}} \\ $$$$\left.\mathrm{2}\right)\:{let}\:{A}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:{u}_{{k}} \:\:\:\:\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$
Commented by math khazana by abdo last updated on 03/Sep/18
A_n =Σ_(k=0) ^n  ∣u_k ∣
$${A}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:\mid{u}_{{k}} \mid \\ $$

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