2003 AMC 10B Problems/Problem 3
Problem
The sum of consecutive even integers is less than the sum of the first consecutive odd counting numbers. What is the smallest of the even integers?
Solution
It is a well-known fact that the sum of the first odd numbers is . This makes the sum of the first odd numbers equal to .
Let be equal to the smallest of the even integers. Then is the next highest, even higher, and so on.
This sets up the equation
Now we solve:
Thus, the smallest integer is .
See Also
2003 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
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