Question

两个数的调和平均数可由“它们乘积的两倍除以它们的和”来计算。 $1$ 与 $2016$ 的调和平均数最接近哪个整数？

The harmonic mean of two numbers can be computed as twice their product divided by their sum. The harmonic mean of $1$ and $2016$ is closest to which integer?

$2$

$45$

$504$

$1008$

$2015$

答案：A

知识点：调和平均数分数估算

难度评级：1020

解答：

调和平均数为 $\dfrac{2\cdot1\cdot2016}{1+2016}=\dfrac{4032}{2017}$ 因为 $\dfrac{2016}{2017}$ 非常接近 $1$ ，所以这个数略小于 $2$ 最接近的整数是 $2$ 。

所以正确答案是 A。

The harmonic mean is $\dfrac{2\cdot1\cdot2016}{1+2016}=\dfrac{4032}{2017}.$ Since $\dfrac{2016}{2017}$ is very close to $1,$ this is just under $2,$ so the closest integer is $2.$

Thus, the correct answer is A.

2016 AMC 12B 第 2 题

答案：A

难度评级：1020

解答：

其他年份的第 2 题