Value of $y=\sqrt{4 + \sqrt[3]{4+\sqrt[4]{4+\sqrt[5]{4+\ldots}}}}$
The question is pretty close to this one, just replace $\,2\,$ by $\,4\,$ in:
There is a little (Delphi Pascal) computer program in
one of the answers. At the end of that piece of code we find:
begin
anatoly(2,13); { at double precision }
end.
Replace this by:
begin
anatoly(4,13); { at double precision }
end.
To get:
4.00000000000000E+0000 2.40161552602630E+0000 +/- 1.80950091432944E-0018
Which is - no big surprise - in concordance with the numerical value as given by
Gottfried Helms
in his answer .