Question

下列哪一项等于

$1 + \cfrac{1}{1 + \cfrac{1}{1 + 1}}$ ？

Which of the following is equal to

$1 + \cfrac{1}{1 + \cfrac{1}{1 + 1}}?$

$\dfrac{5}{4}$

$\dfrac{3}{2}$

$\dfrac{5}{3}$

$2$

$3$

答案：C

知识点：连分数分数

难度评级：870

解答：

从内向外计算， $\begin{aligned} &1 + \cfrac{1}{1 + \cfrac{1}{1 + 1}} \\ &= 1 + \cfrac{1}{1 + \dfrac{1}{2}} \\ &= 1 + \dfrac{1}{\frac{3}{2}} \\ &= 1 + \dfrac{2}{3} = \dfrac{5}{3}. \end{aligned}$

所以正确答案是 C。

Working outward, $\begin{aligned} &1 + \cfrac{1}{1 + \cfrac{1}{1 + 1}} \\ &= 1 + \cfrac{1}{1 + \dfrac{1}{2}} \\ &= 1 + \dfrac{1}{\frac{3}{2}} \\ &= 1 + \dfrac{2}{3} = \dfrac{5}{3}. \end{aligned}$

Thus, the correct answer is C.

2009 AMC 10A 第 3 题

答案：C

难度评级：870

解答：

其他年份的第 3 题