TITLE: Infinite square-rooting
QUESTION [6 upvotes]: $ \lim_{n\to\infty} {\sqrt{1+{\sqrt{2+{\sqrt{\cdots +\sqrt{n}\ }\ }\ }\ }\ \ }\ } = ? $
Either closed answer or an upper bound would help.

REPLY [8 votes]: Unfortunately, our problem is apparently quite a difficult one.