2005 AIME II Problems/Problem 11
Problem
Let be a positive integer, and let be a sequence of integers such that and for Find
Note: Clearly, the stipulation that the sequence is composed of integers is a minor oversight, as the term , for example, is obviously not integral.
Solution
For , we have
.
Thus the product is a monovariant: it decreases by 3 each time increases by 1. Since for we have , so when , will be zero for the first time, which implies that , our answer.
See also
2005 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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