jmc

Question

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

Accepted Answer

We look for a pattern, hoping this sequence either settles down to one number, or that it forms a cycle that repeats. After 1 press, the calculator displays 11 - 5 = -14 After 2 presses, the calculator displays 11 - (-14) = 154 = 45 After 3 presses, the calculator displays 11 - 45 = 115 = 5 Thus, every three presses, the display will be 5. On press 3 33 = 99, the display will be 5. One more press will give -14, which is answer -0.25.