### Instruction: What is the difference between the sum of the first 2003 even counting numbers and the sum of the first 2003 odd counting numbers?### Response: I need to find the sum of the first 2003 even counting numbers and the sum of the first 2003 odd counting numbers.
I know that the sum of the first n even counting numbers is n(n+1), and the sum of the first n odd counting numbers is n^2.
So, the sum of the first 2003 even counting numbers is 2003(2004), and the sum of the first 2003 odd counting numbers is 2003^2.
To find the difference, I need to subtract the smaller sum from the larger one.
Since the even counting numbers are larger than the odd ones, I expect the sum of the evens to be larger than the sum of the odds.
So, the difference is 2003(2004) - 2003^2.
I can factor out 2003 from both terms and simplify: 2003(2004 - 2003) = 2003(1) = 2003.
So, the difference between the sum of the first 2003 even counting numbers and the sum of the first 2003 odd counting numbers is 2003.