Give a precise meaning to evaluate the following:
$$\large{\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\dotsb}}}}}$$
Since I think it has a recursive structure (does it?), I reduce the equation to
$$
p=\sqrt{1+p}
$$
$$
p^2=1+p
$$
$$
p^2-p-1=0
$$
$$
p=\frac{1\pm\sqrt{5}}{2}
$$
Did I do this right?
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