Question Number 31965 by abdo imad last updated on 17/Mar/18
$${find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} \:−\mathrm{2}^{{n}} }{{n}}\:{x}^{{n}} \:\:{with}\:\mid{x}\mid\:<\frac{\mathrm{1}}{\mathrm{2}} \\ $$