Difference between revisions of "2014 UNCO Math Contest II Problems/Problem 2"
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== Solution == | == Solution == | ||
| − | This is asking for the sum of 1-2+3-4...+289. We know that the sum of the first N even numbers is N^2+N. Because there are 144 even numbers less than 289, we take 144^2+144 and get 20880. | + | This is asking for the sum of 1-2+3-4...+289. We know that the sum of the first N even numbers is N^2+N. Because there are 144 even numbers less than 289, we take 144^2+144 and get 20880. Because we're subtracting these, we have -20880. We are also adding the first 145 odd numbers, and the sum of the first N odd numbers is N^2. This is 145^2, so we get 21025. Adding these gives us 145, which is the answer. |
== See also == | == See also == | ||
Revision as of 15:24, 23 December 2014
Problem
Define the Cheshire Cat function 
by
Find the sum 
Solution
This is asking for the sum of 1-2+3-4...+289. We know that the sum of the first N even numbers is N^2+N. Because there are 144 even numbers less than 289, we take 144^2+144 and get 20880. Because we're subtracting these, we have -20880. We are also adding the first 145 odd numbers, and the sum of the first N odd numbers is N^2. This is 145^2, so we get 21025. Adding these gives us 145, which is the answer.
See also
| 2014 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
| All UNCO Math Contest Problems and Solutions | ||
