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