2003 AMC 10A 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

将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

2003

对中的每一对都贡献差

1

。

Each of the

2003

pairs contributes a difference of

1

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.

其他年份的第 1 题