Nested Radicals

From famous Ramanujana Series , we have: $\large \sqrt { 1+2\color{#007fff}{\sqrt { 1+3\sqrt { 1+4\sqrt { 1+5\sqrt{\cdots} } } }} } =3$ $\large 2\color{#007fff}{\sqrt { 1+3\sqrt { 1+4\sqrt { 1+5\sqrt{\cdots} } }}} =9-1$ $\Rightarrow \color{#007fff}{\sqrt { 1+3\sqrt { 1+4\sqrt { 1+5\sqrt{\cdots} } }}} =\huge\boxed{4}$

It was a diverging series as beside √1 +3 every thing becomes negligible so 4x=x^2 And x=4 ans