<s>[INST] Find $f(f(f(f(f(f(\cdots f(x)))))))$ $2018$ times 
I was given a problem to calculate $f(f(f(\dots f(x))))$ $2018$ times if $f(x)=\frac{x}{3} + 3$ and $x=4$. 

Is it even possible to be done without a computer?
 [/INST] Let $x_{n+1} =f(x_n)$ that is  $x_{n+1} =\frac{x_n}{3}+3 $  
Letting $$u_n =x_n -\frac{3}{2}\implies u_{n+1}=\frac13 u_n \implies u_n = \frac{u_1}{3^{n-1}} \implies x_n = \frac{3}{2}+\frac{x_1 -\frac{3}{2}}{3^{n-1}}$$
Hence, we have $$ \color{blue}{ \underbrace{f(f(f(f(f(f(\cdots f(x)))))))}_{n~~times} = x_n = \frac{3}{2}+\frac{2x -3}{2\cdot3^{n-1}}}$$
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