Question Number 50394 by Abdo msup. last updated on 16/Dec/18
![let x∈]0,1[ prove that the equation tan(((πx)/2))=(π/(2nx)) have only one solution x_n 2) study tbe sequence (x_n ) and find a equivalent of x_n](https://www.tinkutara.com/question/Q50394.png)
$$\left.{let}\:\:{x}\in\right]\mathrm{0},\mathrm{1}\left[\:\:{prove}\:{that}\:{the}\:{equation}\right. \\ $$$${tan}\left(\frac{\pi{x}}{\mathrm{2}}\right)=\frac{\pi}{\mathrm{2}{nx}}\:{have}\:{only}\:{one}\:{solution}\:{x}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{study}\:{tbe}\:{sequence}\:\left({x}_{{n}} \right)\:{and}\:{find}\:{a}\:{equivalent}\:{of}\:{x}_{{n}} \\ $$