Have a infinite problem

Calculus Level 3

12×12+1212×12+12×12+1212×=?\sqrt {\frac 12} \times \sqrt{\frac 12 + \frac 12 \sqrt {\frac 12}} \times \sqrt{\frac 12 + \frac 12 \times\sqrt{\frac 12 + \frac 12 \sqrt {\frac 12}}} \times \cdots = \, ?

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