For $ x \in R, x \neq 0,x \neq 1 ,$ let $f_0(x) =\large\frac{1}{1-x} $ and $f_{n+1}(x) =f_0 (f_n(x)),n =0,1,2$.... Then the value of $f_{100} (3)+f_1\bigg( \large\frac{2}{3}\bigg) +f_2 \bigg( \large\frac{3}{2}\bigg)$ is equal to :

Question

$\begin{array}{1 1} (1) \large\frac{8}{3} \\ (2) \large\frac{5}{3} \\ (3) \large\frac{4}{3} \\ (4) \large\frac{1}{3} \end{array} $