Question

下列乘积是多少？ $\dfrac{3}{2}\times\dfrac{4}{3}\times\dfrac{5}{4}\times\cdots\times\dfrac{2006}{2005}$

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

$1$

$1002$

$1003$

$2005$

$2006$

每个分数的分子都会与下一个分数的分母约掉。最后只剩 $\dfrac{2006}{2} = 1003.$

所以正确答案是 C。

Note that the numerator of every fraction cancels with the denominator of the following fraction. This leaves two numbers: $\dfrac{2006}{2} = 1003.$

Thus, C is the correct answer.