Modifying Ramanujan

Algebra Level 3

$\sqrt { 1+1\sqrt { 1+2\sqrt { 1+3\sqrt { 1+4\sqrt { 1+5... } } } } } = \ ?$

The answer is 2.

1 solution

First Last
Dec 22, 2015

From Ramanujan we know $x = 3 =$ $\sqrt{1+2\sqrt{1+3\sqrt{...}}}$ .

So $\sqrt{1+1x} = \sqrt{4} = \boxed{2}$