2 and its square root

Algebra Level 3

\[\sqrt { 2+\sqrt { 2 } +\sqrt { 2+\sqrt { 2 } +\sqrt { 2+\sqrt { 2 } +\ldots } } } \] The value of above expression is in the form \(\sqrt { a } +b\), where \(a\) and \(b\) are integers, find \(a+b\).

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