1994 AIME Problems/Problem 4
Problem
Find the positive integer for which (For real , is the greatest integer )
Solution
Note that if for some , then .
Thus, there are integers such that . So the sum of for all such is .
Let be the integer such that . So for each integer , there are integers such that , and there are such integers such that .
Therefore, .
Through computation: and . Thus, .
So, .
Alternatively, one could notice this is an arithmetico-geometric series and avoid a lot of computation.
See also
1994 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
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