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(\sqrt { 2+\sqrt { 2+\sqrt { 2+......_{ (n\quad times) } } } } =2-4f^{ 2 }(n+2).\ \ As\quad n\rightarrow \infty ,\quad value\quad of\quad { 2 }^{ n }f(n)\quad converges\quad to\quad \frac { \pi }{ k } .\ Find\quad k.)\

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