Question Number 141577 by qaz last updated on 20/May/21
$$\left(\frac{\mathrm{1}}{\mathrm{1}\centerdot\mathrm{2}\centerdot\mathrm{3}}\right)^{\mathrm{2}} +\left(\frac{\mathrm{1}}{\mathrm{2}\centerdot\mathrm{3}\centerdot\mathrm{4}}\right)^{\mathrm{2}} +\left(\frac{\mathrm{1}}{\mathrm{3}\centerdot\mathrm{4}\centerdot\mathrm{5}}\right)^{\mathrm{2}} +...=\frac{\mathrm{1}}{\mathrm{16}}\left(\mathrm{4}\pi^{\mathrm{2}} −\mathrm{39}\right) \\ $$