2003 AMC 12A 第 1 题

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

把每个偶数与它前面的那个奇数配对。

Pair each even number with the odd number just below it

每一对都相差

1

，共有

2003

对。

Each of the

2003

pairs differs by

1

第

k

个正偶数是

2k

，第

k

个正奇数是

2k-1

，二者相差

1

。

把

2003

对的差相加，得到

2003 \cdot 1 = 2003

。

所以正确答案是 D。

The

k

th even counting number is

2k

and the

k

th odd counting number is

2k-1,

which differ by

1.

Summing this difference over all

2003

pairs gives

2003 \cdot 1 = 2003.

Thus, the correct answer is D.

其他年份的第 1 题