The value of the following series is S. Find pi

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$$S=\sqrt \frac{1}{2}\sqrt {\frac{1}{2}+ \frac{1}{2}\sqrt \frac{1}{2}}\sqrt {\frac{1}{2}+ \frac{1}{2}\sqrt {\frac{1}{2}+ \sqrt \frac{1}{2}}} . . .$$

Answer is 2. Please help. I tried taking log but it was not fruitful.