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Question Number 169713 by mathlove last updated on 06/May/22

Commented by Shrinava last updated on 06/May/22

$$\mathrm{E}=2018$$

Commented by mathlove last updated on 07/May/22

$$howis???$$

Commented by mr W last updated on 07/May/22

$$generally$$$$x+n=$$$$=\sqrt{{(x+n)}^2}$$$$=\sqrt{1+{(x+n)}^2-1}$$$$=\sqrt{1+(x+n-1)(x+n+1)}$$$$=\sqrt{1+(x+n-1)\sqrt{1+(x+n)(x+n+2)}}$$$$=\sqrt{1+(x+n-1)\sqrt{1+(x+n)\sqrt{1+(x+n+1)(x+n+3)}}}$$$$....$$$$withx=2017,n=1$$$$2018=\sqrt{1+2017\sqrt{1+2018\sqrt{1+2019\sqrt{1+2020\sqrt{1+...}}}}}$$

Commented by mathlove last updated on 07/May/22

$$thanksmrW$$

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