Question Number 89934 by ~blr237~ last updated on 20/Apr/20
![Let x∈]0;1[ Prove that Σ_(n=1) ^∞ (x^n /(1+x^n )) +Σ_(n=1) ^∞ (((−x)^n )/(1−x^n )) = 0](https://www.tinkutara.com/question/Q89934.png)
$$\left.{Let}\:{x}\in\right]\mathrm{0};\mathrm{1}\left[\:\:{Prove}\:{that}\right. \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{x}^{{n}} }{\mathrm{1}+{x}^{{n}} }\:+\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−{x}\right)^{{n}} }{\mathrm{1}−{x}^{{n}} }\:=\:\mathrm{0} \\ $$