Question Number 133381 by Dwaipayan Shikari last updated on 21/Feb/21
$$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{2}} }\left(\frac{\mathrm{1}}{\mathrm{2}.\mathrm{1}!}\right)+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }\left(\frac{\mathrm{1}.\mathrm{3}}{\mathrm{2}^{\mathrm{2}} .\mathrm{2}!}\right)+\frac{\mathrm{1}}{\mathrm{5}^{\mathrm{2}} }\left(\frac{\mathrm{1}.\mathrm{3}.\mathrm{5}}{\mathrm{2}^{\mathrm{3}} .\mathrm{3}!}\right)+...=\frac{\pi}{\mathrm{2}}{log}\left(\mathrm{2}\right) \\ $$