Difference between revisions of "2016 AMC 8 Problems/Problem 8"
Pi is 3.14 (talk | contribs) |
Elijahman112 (talk | contribs) (→Video Solution by savannahsolver) |
||
(4 intermediate revisions by 4 users not shown) | |||
Line 20: | Line 20: | ||
==Video Solution== | ==Video Solution== | ||
+ | |||
+ | https://youtu.be/iuUwextm334?si=LrUYCG3Cvo0zKqym | ||
+ | |||
+ | A solution so simple a 12-year-old made it! | ||
+ | |||
+ | ~Elijahman~ | ||
+ | |||
+ | ==Video Solution by savannahsolver== | ||
https://youtu.be/TwIwA0XkzoI | https://youtu.be/TwIwA0XkzoI | ||
Latest revision as of 11:49, 20 June 2024
Contents
Problem
Find the value of the expression
Solutions
Solution 1
We can group each subtracting pair together:
After subtracting, we have:
There are
even numbers, therefore there are
even pairs. Therefore the sum is
Solution 2
Since our list does not end with one, we divide every number by 2 and we end up with
We can group each subtracting pair together:
There are now
pairs of numbers, and the value of each pair is
. This sum is
. However, we divided by
originally so we will multiply
to get the final answer of
Video Solution
https://youtu.be/iuUwextm334?si=LrUYCG3Cvo0zKqym
A solution so simple a 12-year-old made it!
~Elijahman~
Video Solution by savannahsolver
~savannahsolver
Video Solution by OmegaLearn
https://youtu.be/51K3uCzntWs?t=645
~ pi_is_3.14
See Also
2016 AMC 8 (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 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.