Question Number 169713 by mathlove last updated on 06/May/22
Commented by Shrinava last updated on 06/May/22
$$\mathrm{E}\:=\:\mathrm{2018} \\ $$
Commented by mathlove last updated on 07/May/22
$${how}\:{is}??? \\ $$
Commented by mr W last updated on 07/May/22
$${generally} \\ $$$${x}+{n}= \\ $$$$=\sqrt{\left({x}+{n}\right)^{\mathrm{2}} } \\ $$$$=\sqrt{\mathrm{1}+\left({x}+{n}\right)^{\mathrm{2}} −\mathrm{1}} \\ $$$$=\sqrt{\mathrm{1}+\left({x}+{n}−\mathrm{1}\right)\left({x}+{n}+\mathrm{1}\right)} \\ $$$$=\sqrt{\mathrm{1}+\left({x}+{n}−\mathrm{1}\right)\sqrt{\mathrm{1}+\left({x}+{n}\right)\left({x}+{n}+\mathrm{2}\right)}} \\ $$$$=\sqrt{\mathrm{1}+\left({x}+{n}−\mathrm{1}\right)\sqrt{\mathrm{1}+\left({x}+{n}\right)\sqrt{\mathrm{1}+\left({x}+{n}+\mathrm{1}\right)\left({x}+{n}+\mathrm{3}\right)}}} \\ $$$$…. \\ $$$${with}\:{x}=\mathrm{2017},\:{n}=\mathrm{1} \\ $$$$\mathrm{2018}=\sqrt{\mathrm{1}+\mathrm{2017}\sqrt{\mathrm{1}+\mathrm{2018}\sqrt{\mathrm{1}+\mathrm{2019}\sqrt{\mathrm{1}+\mathrm{2020}\sqrt{\mathrm{1}+…}}}}} \\ $$
Commented by mathlove last updated on 07/May/22
$${thanks}\:{mrW} \\ $$