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Question Number 33358 by caravan msup abdo. last updated on 15/Apr/18

prove that Σ_(p=1) ^∞  (z^p /(1+z^p )) =Σ_(q=1) ^∞  (−1)^(q−1) (z^q /(1−z^q ))

$${prove}\:{that}\:\sum_{{p}=\mathrm{1}} ^{\infty} \:\frac{{z}^{{p}} }{\mathrm{1}+{z}^{{p}} }\:=\sum_{{q}=\mathrm{1}} ^{\infty} \:\left(−\mathrm{1}\right)^{{q}−\mathrm{1}} \frac{{z}^{{q}} }{\mathrm{1}−{z}^{{q}} } \\ $$

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