2020 AMC 8 Problems/Problem 12
Contents
Problem
For a positive integer , the factorial notation represents the product of the integers from to . (For example, .) What value of satisfies the following equation?
Solution 1
We have , and . Therefore the equation becomes , and so . Cancelling the s, it is clear that .
Solution 2 (variant of Solution 1)
Since , we obtain , which becomes and thus . We therefore deduce .
Solution 3 (using answer choices)
We can see that the answers to contain a factor of , but there is no such factor of in . Therefore, the answer must be .
Video Solution
See also
2020 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 11 |
Followed by Problem 13 | |
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