Question Number 33301 by abdo imad last updated on 14/Apr/18
$${calculate}\:\:\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left(\pi{nx}\right)}{\mathrm{2}^{{n}} }\:\:{and}\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{{sin}\left(\pi{nx}\right)}{\mathrm{2}^{{n}} } \\ $$