Question

如果乘积那么 $a$ 与 $b$ 的和是多少？ $\dfrac{3}{2}\cdot \dfrac{4}{3}\cdot \dfrac{5}{4}\cdot \dfrac{6}{5}\cdot \ldots\cdot \dfrac{a}{b} = 9,$

If the product $\dfrac{3}{2}\cdot \dfrac{4}{3}\cdot \dfrac{5}{4}\cdot \dfrac{6}{5}\cdot \ldots\cdot \dfrac{a}{b} = 9,$ what is the sum of $a$ and $b?$

$11$

$13$

$17$

$35$

$37$

答案：D

知识点：裂项相消分数

难度评级：1340

解答：

每个分数的分子都会与右边分数的分母约掉。

全部约分后得到 $\dfrac{a}{2} = 9 \Rightarrow a = 18 \Rightarrow b = 17.$

所求和为 $18 + 17 = 35.$

所以正确答案是 D。

Note that the numerator of each fraction cancels with the denominator of the fraction to its right.

We can then cancel out all these terms to get a final equation of $\dfrac{a}{2} = 9 \Rightarrow a = 18 \Rightarrow b = 17.$

The desired sum is then $18 + 17 = 35.$

Thus, D is the correct answer.

1997 AMC 8 第 19 题

答案：D

难度评级：1340

解答：

其他年份的第 19 题