Question

下列表达式的值是多少？

$\begin{aligned} &2(2(2(2(2(2+1)+1)\\ &\qquad{}+1)+1)+1)+1 \end{aligned}$

What is the value of the following expression?

$\begin{aligned} &2(2(2(2(2(2+1)+1)\\ &\qquad{}+1)+1)+1)+1 \end{aligned}$

$70$

$97$

$127$

$159$

$729$

从最内层括号开始向外计算。

Work from the innermost parentheses outward

注意中间结果都是二的幂减一。

Notice the intermediate values are one less than powers of two

从最内层的 $2+1$ 开始，每向外一层，就把当前值乘以二再加 $1$ 。依次得到 $3,7,15,31,63,127\text{。}$

所以正确答案是 C。

Starting with the innermost $2+1,$ each new layer doubles the current value and adds $1.$ The successive values are $3,7,15,31,63,127.$

Thus, C is the correct answer.