Difference between revisions of "2024 SSMO Speed Round Problems/Problem 7"
(Created page with "==Problem== Let <math>S</math> denote the set of all ellipses centered at the origin and with axes <math>AB</math> and <math>CD</math> where <math>A=(-x,0),B=(x,0),C=(0,-y),<...") |
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==Solution== | ==Solution== | ||
| + | The answer is <cmath>\left(\left(\sum_{i=0}^{10}(-1)^ii^2\right)\left(\sum_{i=0}^{10}(-1)^ii^2\right)\right) = \left(\sum_{i=0}^{10}i\right) = \boxed{3025}.</cmath> | ||
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| + | ~SMO_Team | ||
Latest revision as of 14:27, 10 September 2025
Problem
Let 
denote the set of all ellipses centered at the origin and with axes 
and 
where 
and 
for 
and 
Let 
denote the set of similar ellipses centered at the origin and passing through 
for 
and 
If the positive difference between the sum of the areas of all ellipses in and the sum of the areas of all the ellipses in is 
find 
Solution
The answer is ![\[\left(\left(\sum_{i=0}^{10}(-1)^ii^2\right)\left(\sum_{i=0}^{10}(-1)^ii^2\right)\right) = \left(\sum_{i=0}^{10}i\right) = \boxed{3025}.\]](http://latex.artofproblemsolving.com/2/4/e/24e86bce5ce759446114ea4409f61fa25646e11a.png)
~SMO_Team
