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Infinitely nested radicals posed by Ramanujan

### Solution

Solution by the mathematician

**Srinivasa Ramanujan**:\[n(n+2)=n\sqrt{1+(n+1)(n+3)}\] Let \(n(n+2)=f(n)\)

\[\Rightarrow n(n+2)=n \sqrt{1+(n+1)\sqrt{1+(n+2)\sqrt{1+(n+3)\sqrt{1+\cdot\cdot\cdot}}}}
\]

Putting \(n=1
\), we get \[\large \sqrt{1+2\sqrt{1+3\sqrt{1+\cdot\cdot\cdot}}}=3
\]

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