Infinite Fractions - 5

Calculus Level 3

$\Large \cfrac { 1+\frac { 1+\frac { 1+\cdots }{ \sqrt { 1+\cdots } } }{ \sqrt { 1+\frac { 1+\cdots }{ \sqrt { 1+\cdots } } } } }{ \sqrt { 1+\frac { 1+\frac { 1+\cdots }{ \sqrt { 1+\cdots } } }{ \sqrt { 1+\frac { 1+\cdots }{ \sqrt { 1+\cdots } } } } } } = \, ?$

Give your answer to 3 decimal places.