AMC10 2003 A

AMC10 2003 A · Q1

AMC10 2003 A · Q1. It mainly tests Arithmetic sequences basics, Arithmetic misc.

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

前2003个偶数计数数的和与前2003个奇数计数数的和的差是多少？

(A) 0 0

(B) 1 1

(D) 2003 2003

(E) 4006 4006

Answer

Correct choice: (D)

正确答案：（D）

Solution

Each even counting number, beginning with 2, is one more than the preceding odd counting number. Therefore the difference is $(1)(2003) = 2003$.

每个偶数计数数，从2开始，比前一个奇数计数数多1。因此差值为$(1)(2003) = 2003$。

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