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

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