2003 AMC 10A Problems/Problem 1

Problem

What is the difference between the sum of the first $2003$ even counting numbers and the sum of the first $2003$ odd counting numbers?

$\mathrm{(A) \ } 0\qquad \mathrm{(B) \ } 1\qquad \mathrm{(C) \ } 2\qquad \mathrm{(D) \ } 2003\qquad \mathrm{(E) \ } 4006$

The first $2003$ even counting numbers are $2,4,6,...,4006$ .

The first $2003$ odd counting numbers are $1,3,5,...,4005$ .

Thus, the problem is asking for the value of $(2+4+6+...+4006)-(1+3+5+...+4005)$ .

$(2+4+6+...+4006)-(1+3+5+...+4005) = (2-1)+(4-3)+(6-5)+...+(4006-4005)$

$= 1+1+1+\ldots+1 = 2003 \Rightarrow \mbox{D}$