For x ∈ R, x ≠ 0, x ≠ 1, let f_0(x)=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(2/3)+f_2(3/2) is equal to:

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