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?

if $f(x)=\frac{x}{3}+3$
Then $f^2(x)=\frac{f(x)}{3}+3=\frac{x}{9}+\frac{3}{3}+3$
and $f^3(x)=\frac{f^2(x)}{3}+4=\frac{x}{27}+\frac{3}{9}+\frac{3}{3}+3$
By induction the general form is emerging as:
$$f^n(x)=3^{-n}x+3\left(\sum_{k=1}^n3^{1-k}\right)$$
Use the formula for a geometric sum and plug in $x=4, n=2018$:
$f^{2018}(4)=4+\frac{1}{2}\left(1-3^{-2018}\right)$
