Standard results won't help you in this

Calculus Level 5

Given a function ff defined as f(x)=x+12,f(x)=\sqrt { \frac { x+1 }{ 2 } }, find the value of

limn22n+1(1fn(1)).\lim _{ n\rightarrow \infty }{ { 2 }^{ 2n+1 }(1-{ f }^{ n }(-1)) }.

Details and Assumptions

  • fn(x)(f(x))n{ f }^{ n }(x)\neq { (f(x)) }^{ n } it is the composite function taken nn times. For example: f3(x)=f(f(f(x))){ f }^{ 3 }(x)=f(f(f(x))).
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