2015 AIME II Problems/Problem 13
Problem
Define the sequence by , where represents radian measure. Find the index of the 100th term for which .
Solution
If , . Then if satisfies , , and Since is positive, it does not affect the sign of . Let . Now since and , is negative if and only if , or when . Since is irrational, there is always only one integer in the range, so there are values of such that at . Then the hundredth such value will be when and .
See also
2015 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
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