Standard results won't help you in this

Calculus Level 5

Given a function \(f\) defined as \(f(x)=\sqrt { \frac { x+1 }{ 2 } },\) find the value of

\[\lim _{ n\rightarrow \infty }{ { 2 }^{ 2n+1 }(1-{ f }^{ n }(-1)) }.\]

Details and Assumptions

  • \({ f }^{ n }(x)\neq { (f(x)) }^{ n }\) it is the composite function taken \(n\) times. For example: \({ f }^{ 3 }(x)=f(f(f(x)))\).
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