Question Number 29985 by abdo imad last updated on 14/Feb/18
$${prove}\:{that}\:\:\:\:\sum_{{p}=\mathrm{1}} ^{\infty} \:\:\:\:\:\:\frac{{a}^{{p}} }{\mathrm{1}−{a}^{\mathrm{2}{p}} }\:=\:\sum_{{p}=\mathrm{1}} ^{\infty} \:\:\:\:\frac{{a}^{\mathrm{2}{p}−\mathrm{1}} }{\mathrm{1}−{a}^{\mathrm{2}{p}−\mathrm{1}} }\:. \\ $$