How do you prove the identity(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

3 = \sqrt{1 + 2\sqrt{1 + 3\sqrt{1+4\sqrt{1 + \cdots}}}}

[/tex]

with a real proof that actually proves the convergence? I know there are "proofs" that "prove" the identity with some trickery that ignore all the convergence issues, and I'm not interested in those trickeries.

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# I Ramanujan square roots

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