Roots Nested Without End

Define a sequence by b1=2 b_1 = \sqrt{2} and bn+1=2+bn b_{n+1} = \sqrt{2 + b_n} , so that the terms build the infinite nested radical 2+2+2+⋯. \sqrt{2 + \sqrt{2 + \sqrt{2 + \cdots}}}. What value does this expression converge to?

Answer

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