Difference between revisions of "2013 AMC 8 Problems/Problem 3"
(→Solution) |
Pi is 3.14 (talk | contribs) |
||
| (8 intermediate revisions by 6 users not shown) | |||
| Line 5: | Line 5: | ||
==Solution== | ==Solution== | ||
| + | We group the addends inside the parentheses two at a time: | ||
| + | <cmath> | ||
| + | \begin{align*} | ||
| + | -1 + 2 - 3 + 4 - 5 + 6 - 7 + \ldots + 1000 &= (-1 + 2) + (-3 + 4) + (-5 + 6) + \ldots + (-999 + 1000) \\ | ||
| + | &= \underbrace{1+1+1+\ldots + 1}_{\text{500 1's}} \\ | ||
| + | &= 500. | ||
| + | \end{align*} | ||
| + | </cmath> | ||
| + | Then the desired answer is <math>4 \times 500 = \boxed{\textbf{(E)}\ 2000}</math>. | ||
| + | |||
| + | ==Video Solution== | ||
| + | https://youtu.be/4Gy1CrYTDHA ~savannahsolver | ||
| + | |||
| + | ==Video Solution by OmegaLearn== | ||
| + | https://youtu.be/TkZvMa30Juo?t=3074 | ||
| + | |||
| + | ~ pi_is_3.14 | ||
| − | |||
| − | |||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2013|num-b=2|num-a=4}} | {{AMC8 box|year=2013|num-b=2|num-a=4}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Latest revision as of 00:01, 26 December 2022
Problem
What is the value of 
?
Solution
We group the addends inside the parentheses two at a time:
Then the desired answer is 
.
Video Solution
https://youtu.be/4Gy1CrYTDHA ~savannahsolver
Video Solution by OmegaLearn
https://youtu.be/TkZvMa30Juo?t=3074
~ pi_is_3.14
See Also
| 2013 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 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. 
