Difference between revisions of "2000 AIME II Problems/Problem 15"
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Revision as of 19:31, 4 July 2013
Problem
Find the least positive integer such that
Solution
We apply the identity
The motivation for this identity arises from the need to decompose those fractions, possibly into telescoping series.
Thus our summation becomes
Since , the summation simply reduces to . Therefore, the answer is .
See also
2000 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Last Question | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
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