$$\sqrt{1+\sqrt{2+\sqrt{3+\sqrt{4+\sqrt{5+\sqrt{ \dots }}}}}}$$ I don't understand how to solve that. I mean I don't know where to begin. Tell me if this infinite radical has a solution or converge to a number. Thanks.
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See e.g. Nested Radical Constant and references there. – Robert Israel Dec 05 '16 at 16:06
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1Not sure, where exactly this was asked here, but I am pretty sure that it is a duplicate. – Peter Dec 05 '16 at 16:06
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You could also see here and here. – Dec 05 '16 at 16:10
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Is it a constant? Wow – Isai Dávila Cuba Dec 05 '16 at 16:10
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i hope it can help you
Theorem (Herschfeld, 1935).
The sequence $u_{n}$=$\sqrt{a_1+\sqrt{a_2+.....+\sqrt{a_{n}}}}$
converges if and only if
$\lim_{n\to∞} sup a^{2^{-n}}_{n} \lt ∞ $
The American Mathematical Monthly, Vol. 42, No. 7 (Aug-Sep 1935), 419-429.
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