# 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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