Difference between revisions of "2002 AMC 10A Problems/Problem 16"
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+ | ==Video Solution by Daily Dose of Math== | ||
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+ | https://youtu.be/X1pdpIGSFRU | ||
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+ | ~Thesmartgreekmathdude | ||
==See Also== | ==See Also== |
Latest revision as of 08:57, 1 September 2024
Contents
[hide]Problem
Let . What is ?
Solution 1
Let . Since one of the sums involves and it makes sense to consider . We have . Rearranging, we have , so . Thus, our answer is .
Solution 2
Take . Now we can clearly see: . Continuing this same method with , and we get: , , , and , Adding, we see . Therefore, .
Solution 3(Video solution using [The Apple Method])
https://www.youtube.com/watch?v=rz86M2hlOGk&feature=emb_logo https://youtu.be/NRdOxPUDngI
Video Solution by OmegaLearn
https://youtu.be/tKsYSBdeVuw?t=4105
~ pi_is_3.14
Video Solution by Daily Dose of Math
~Thesmartgreekmathdude
See Also
2002 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 15 |
Followed by Problem 17 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.