\(Let\)

\[\begin{align} u_1 & = 0 \\ u_{n + 1} & = \sqrt{(1 + u_{n})/2} \\ P_{n} & = 2^{n + 1} \sqrt{2 (1 - u_{n}}) \end{align} \]

\(Find\) \(\lim_{n\to\infty}P_{n}\) \((express\) \(the\) \(answer\) \(to\) \(two\) \(decimal\) \(places).\)

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