Question

下列表达式的值是多少？

$\cfrac{1}{1 + \cfrac{1}{2 + \cfrac{1}{3}}}$

What is the value of the following expression?

$\cfrac{1}{1 + \cfrac{1}{2 + \cfrac{1}{3}}}$

$\dfrac16$

$\dfrac{3}{10}$

$\dfrac{7}{10}$

$\dfrac56$

$\dfrac{10}{3}$

从里面开始， $2 + \dfrac13 = \dfrac73$ ，所以 $\dfrac{1}{7/3} = \dfrac37$ 。

接着 $1 + \dfrac37 = \dfrac{10}{7}$ ，整个表达式为 $\dfrac{1}{10/7} = \dfrac{7}{10}$ 。

所以正确答案是 C。

Starting inside, $2 + \dfrac13 = \dfrac73,$ so $\dfrac{1}{7/3} = \dfrac37.$

Then $1 + \dfrac37 = \dfrac{10}{7},$ and the whole expression is $\dfrac{1}{10/7} = \dfrac{7}{10}.$

Thus, the correct answer is C .