Question Number 51986 by maxmathsup by imad last updated on 01/Jan/19
$$\left.\mathrm{1}\right)\:{prove}\:{that}\:{thx}\:=\frac{\mathrm{2}}{{th}\left(\mathrm{2}{x}\right)}\:−\frac{\mathrm{1}}{{th}\left({x}\right)} \\ $$$$\left.\mathrm{2}\right){simplify}\:\:{S}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:\mathrm{2}^{{k}} {th}\left(\mathrm{2}^{{k}} {x}\right) \\ $$