Infinite Fractions - 5

Calculus Level 3

1+1+1+1+1+1+1+1+1+1+1+1+1+1+=? \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.

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