Difference between revisions of "2020 AIME II Problems/Problem 8"
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==Problem== | ==Problem== | ||
Define a sequence recursively by <math>f_1(x)=|x-1|</math> and <math>f_n(x)=f_{n-1}(|x-n|)</math> for integers <math>n>1</math>. Find the least value of <math>n</math> such that the sum of the zeros of <math>f_n</math> exceeds <math>500,000</math>. | Define a sequence recursively by <math>f_1(x)=|x-1|</math> and <math>f_n(x)=f_{n-1}(|x-n|)</math> for integers <math>n>1</math>. Find the least value of <math>n</math> such that the sum of the zeros of <math>f_n</math> exceeds <math>500,000</math>. | ||
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==See Also== | ==See Also== | ||
{{AIME box|year=2020|n=II|num-b=7|num-a=9}} | {{AIME box|year=2020|n=II|num-b=7|num-a=9}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 02:19, 8 June 2020
Problem
Define a sequence recursively by 
and 
for integers 
. Find the least value of 
such that the sum of the zeros of 
exceeds 
.
See Also
| 2020 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 7 |
Followed by Problem 9 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
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