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| − | == | + | ==IMAPnis Problem 6.9== |
{{AMC10 Problems|year=2021|ab=A}} | {{AMC10 Problems|year=2021|ab=A}} | ||
| + | A number <math>\epsilon</math> is said to be <i>special</i> if | ||
| + | <cmath>\lim_{q \to\infty} \frac{\cos \left( \sum_{k=0}^{\epsilon} \sqrt{ \frac{\epsilon ^ {k \epsilon + q}}{\epsilon \cdot \pi \cdot x} } \right)}{(2x+4) \lfloor qx \rfloor}</cmath> | ||
| + | is true for all <math>x</math>. | ||
| + | Find all <i>special</i> numbers. | ||
Revision as of 16:28, 30 July 2021
IMAPnis Problem 6.9
| 2021 AMC 10A (Answer Key) Printable versions: • AoPS Resources • PDF | ||
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Instructions
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A number 
is said to be special if
![\[\lim_{q \to\infty} \frac{\cos \left( \sum_{k=0}^{\epsilon} \sqrt{ \frac{\epsilon ^ {k \epsilon + q}}{\epsilon \cdot \pi \cdot x} } \right)}{(2x+4) \lfloor qx \rfloor}\]](http://latex.artofproblemsolving.com/a/c/9/ac98c42cf35422faca742c3b49a024475e5bdfd3.png)
is true for all 
.
Find all special numbers.
