Question 1009869
.
<pre>
Are you talking about 

{{{sqrt(2 + sqrt(2 + sqrt(2 + ellipsis)))}}} ?

If "Yes", then introduce x = {{{sqrt(2 + sqrt(2 + sqrt(2 + ellipsis)))}}}.

Square both sides, and you will get an equation

{{{x^2}}} = {{{2 +x}}},   or

{{{x^2 - x - 2}}} = {{{0}}}.

Factorize left side

(x+1)*(x-2) = 0.

The appropriate root is x = 2.

So,  {{{sqrt(2 + sqrt(2 + sqrt(2 + ellipsis)))}}} = 2.

<U>Answer</U>.  {{{sqrt(2 + sqrt(2 + sqrt(2 + ellipsis)))}}} = 2.
</pre>