MathDB
1996 AJHSME Problem 20

Source:

July 10, 2011
AMC

Problem Statement

Suppose there is a special key on a calculator that replaces the number xx currently displayed with the number given by the formula 11−x\frac{1}{1-x}. For example, if the calculator is displaying 22 and the special key is pressed, then the calculator will display −1-1 since 11−2=−1\frac{1}{1-2}=-1. Now suppose that the calculator is displaying 55. After the special key is pressed 100 times in a row, the calculator will display
(A) −0.25(B) 0(C) 0.8(D) 1.25(E) 5\text{(A)}\ -0.25 \qquad \text{(B)}\ 0 \qquad \text{(C)}\ 0.8 \qquad \text{(D)}\ 1.25 \qquad \text{(E)}\ 5
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