Question Number 129145 by Dwaipayan Shikari last updated on 13/Jan/21
$$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}^{\mathrm{2}} }{\mathrm{1}+\frac{\mathrm{2}^{\mathrm{2}} }{\mathrm{1}+\frac{\mathrm{3}^{\mathrm{2}} }{\mathrm{1}+\frac{\mathrm{4}^{\mathrm{2}} }{\mathrm{1}+\frac{\mathrm{5}^{\mathrm{2}} }{\mathrm{1}+...}}}}}} \\ $$
Commented by Dwaipayan Shikari last updated on 13/Jan/21
$${log}\left(\mathrm{2}\right) \\ $$