Nested radicals notation

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Is there any convenient notation for things like: $\sqrt{1+\sqrt{2+{\sqrt{3+\cdots}}}}$

Maybe using limits?

I'm asking purely notational-wise.

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$\sqrt{1+\sqrt{2+\sqrt{\dots}}}=\lim_{n\rightarrow\infty}\sqrt{1+\sqrt{2+\sqrt{\dots+\sqrt{n}}}}$