1984 AHSME Problems/Problem 11
Problem
A calculator has a key that replaces the displayed entry with its square, and another key which replaces the displayed entry with its reciprocal. Let be the final result when one starts with a number and alternately squares and reciprocates times each. Assuming the calculator is completely accurate (e.g. no roundoff or overflow), then equals
Solution
Notice that taking the reciprocal of a number is equivalent to raising the number to the power. Therefore, taking the reciprocal of a number and then squaring it is . Also, since multiplication is commutative, this is equivalent to squaring the number then taking the reciprocal of it. Doing this times equals .
See Also
1984 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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