Question

前 $2003$ 个正偶数的和与前 $2003$ 个正奇数的和相差多少？

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

$0$

$1$

$2$

$2003$

$4006$

第 $k$ 个正偶数 $2k$ 正好比第 $k$ 个正奇数 $2k-1$ 大 $1$ 。

对 $2003$ 对求和，差为 $2003 \cdot 1 = 2003$ 。

所以正确答案是 D。

The $k$ th even number $2k$ is exactly $1$ more than the $k$ th odd number $2k-1.$

Summing this difference over all $2003$ pairs gives $2003 \cdot 1 = 2003.$

Thus, the correct answer is D.