Question

求下式的值： $\left(\left((2+1)^{-1}+1\right)^{-1}+1\right)^{-1}+1?$

What is the value of $\left(\left((2+1)^{-1}+1\right)^{-1}+1\right)^{-1}+1?$

$\dfrac{5}{8}$

$\dfrac{11}{7}$

$\dfrac{8}{5}$

$\dfrac{18}{11}$

$\dfrac{15}{8}$

答案：B

知识点：分数运算顺序

难度评级：560

解答：

由内向外逐步化简： $\begin{aligned} &\left(\left((2+1)^{-1}+1\right)^{-1}+1\right)^{-1}+1 \\ &=\left(\left(\dfrac{1}{3}+1\right)^{-1}+1\right)^{-1}+1 \\ &=\left(\dfrac{3}{4}+1\right)^{-1}+1 \\ &=\dfrac{4}{7} + 1 \\ &=\dfrac{11}{7} \end{aligned}$

因此正确答案是 B。

We can simplify this as follows. $\begin{aligned} &\left(\left((2+1)^{-1}+1\right)^{-1}+1\right)^{-1}+1 \\ &=\left(\left(\dfrac{1}{3}+1\right)^{-1}+1\right)^{-1}+1 \\ &=\left(\dfrac{3}{4}+1\right)^{-1}+1 \\ &=\dfrac{4}{7} + 1 \\ &=\dfrac{11}{7} \end{aligned}$

Thus, B is the correct answer.

2018 AMC 10A 第 1 题

答案：B

难度评级：560

解答：

其他年份的第 1 题