AMC8 2006

AMC8 2006 · Q9

AMC8 2006 · Q9. It mainly tests Fractions.

What is the product of $\frac{3}{2} \times \frac{4}{3} \times \frac{5}{4} \times \dots \times \frac{2006}{2005}$?

计算 $\frac{3}{2} \times \frac{4}{3} \times \frac{5}{4} \times \dots \times \frac{2006}{2005}$ 的积？

(A) 1 1

(B) 1002 1002

(D) 2005 2005

(E) 2006 2006

Answer

Correct choice: (C)

正确答案：（C）

Solution

(C) Note that in each fraction, the numerator is the same as the denominator in the next fraction, so they divide. The product of $\frac{3}{2}\times\frac{4}{3}\times\frac{5}{4}\times\cdots\times\frac{2006}{2005}=\frac{2006}{2}=1003.$

（C）注意在每个分数中，分子与下一个分数的分母相同，因此可以相互约去。乘积 $\frac{3}{2}\times\frac{4}{3}\times\frac{5}{4}\times\cdots\times\frac{2006}{2005}=\frac{2006}{2}=1003.$

Topics

AR.001 Fractions