2008 AMC 12A 第 4 题

Question

下列哪一个等于乘积：

\begin{aligned} &\dfrac{8}{4} \cdot \dfrac{12}{8} \cdot \dfrac{16}{12} \\ &\quad \cdots \dfrac{4n + 4}{4n} \cdots \dfrac{2008}{2004} \end{aligned}\text{？}

Which of the following is equal to the product

\begin{aligned} &\dfrac{8}{4} \cdot \dfrac{12}{8} \cdot \dfrac{16}{12} \\ &\quad \cdots \dfrac{4n + 4}{4n} \cdots \dfrac{2008}{2004}? \end{aligned}

251

502

1004

2008

4016

每个分母都会和前一个分数的分子约掉。

Each denominator cancels with the numerator of the previous fraction

最后只剩最后一个分子和第一个分母。

Only the last numerator and the first denominator survive

除第一个分母外，每个分母都与前一个分数的分子相消，所以乘积化为

\dfrac{2008}{4} = 502\text{。}

所以正确答案是 B。

Every denominator except the first cancels with the numerator of the preceding fraction, so the product collapses to

\dfrac{2008}{4} = 502.

Thus, B is the correct answer.

其他年份的第 4 题