\[\large P = \prod_{k=1}^\infty \left( \dfrac{2k}{2k-1} \cdot \dfrac{2k}{2k+1} \right)\]

\[\large I = \displaystyle \int_0^1 \sqrt{1-x^2} \,dx\]

Let \(P\) and \(I\) be as defined above. What is the relation between \(P\) and \(I\)?

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