AMC 8 1996 Problem 20

Suppose there is a special key on a calculator that replaces the number $x$ currently displayed with the number given by the formula $1/(1-x)$. For example, if the calculator is displaying 2 and the special key is pressed, then the calculator will display -1 since $1/(1-2)=-1$. Now suppose that the calculator is displaying 5. After the special key is pressed 100 times in a row, the calculator will display $\text{(A)}\ -0.25 \text{(B)}\ 0 \text{(C)}\ 0.8 \text{(D)}\ 1.25 \text{(E)}\ 5$