Question Number 124861 by Dwaipayan Shikari last updated on 06/Dec/20
$$\frac{\left(\frac{\mathrm{1}}{\mathrm{2}}\right)!}{\left(\frac{\mathrm{3}}{\mathrm{2}}\right)!}−\frac{\left(\frac{\mathrm{3}}{\mathrm{2}}\right)!\mathrm{1}!}{\left(\frac{\mathrm{5}}{\mathrm{2}}\right)!}+\frac{\left(\frac{\mathrm{5}}{\mathrm{2}}\right)!\mathrm{2}!}{\left(\frac{\mathrm{7}}{\mathrm{2}}\right)!}−…. \\ $$