Question Number 139481 by Dwaipayan Shikari last updated on 27/Apr/21
$$\mathrm{1}+\frac{\pi^{\mathrm{6}} }{\mathrm{27}.\mathrm{6}!}+\frac{\pi^{\mathrm{12}} }{\mathrm{27}^{\mathrm{2}} .\mathrm{12}!}+\frac{\pi^{\mathrm{18}} }{\mathrm{27}^{\mathrm{3}} .\mathrm{18}!}+…=\frac{{e}^{\frac{\pi}{\:\sqrt{{a}}}} +{e}^{−\frac{\pi}{\:\sqrt{{a}}}} }{\mathrm{2}{a}} \\ $$$${Find}\:{a} \\ $$