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Nested Radicals

Calculus Level 2

$\sqrt{\frac{2}{2^1}+\sqrt{ \frac{2}{2^2}+\sqrt{\frac{2}{2^4}+\sqrt{\frac{2}{2^8}+\ldots}} }} = \ ?$

\frac{1}{2}

2

\sqrt{\frac{1}{2}}

\sqrt{2}

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