Question Number 32936 by abdo imad last updated on 06/Apr/18
$${let}\:{give}\:\mid{x}\mid<\mathrm{1}\:{prove}\:{that} \\ $$$$\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{{cos}\left({n}\theta\right)}{{n}}\:{x}^{{n}} \:=−\frac{\mathrm{1}}{\mathrm{2}}{ln}\left(\mathrm{1}−\mathrm{2}{xcos}\theta+{x}^{\mathrm{2}} \right)\:. \\ $$