2017 AMC 10A 第 1 题

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.

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