Question Number 122950 by bemath last updated on 21/Nov/20
$$\:\:\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\mathrm{2}\sqrt{\mathrm{3}+...\sqrt{\mathrm{1}+\mathrm{2014}+\sqrt{\mathrm{1}+\mathrm{2015}.\mathrm{2016}}}}}}\:=\:? \\ $$
Commented by Dwaipayan Shikari last updated on 21/Nov/20
$$\mathrm{2} \\ $$$$\sqrt{\mathrm{1}+\mathrm{2}+\sqrt{\mathrm{1}+\mathrm{3}\sqrt{\mathrm{1}+\mathrm{4}\sqrt{...}}}}=\mathrm{3} \\ $$$$\sqrt{\mathrm{1}+\mathrm{3}}=\mathrm{2} \\ $$