Question

的值是多少？ $\begin{aligned} &4 \cdot (-1 + 2 - 3 + 4 - 5 + 6 \\ &\qquad {}- 7 + \cdots + 1000)? \end{aligned}$

What is the value of $\begin{aligned} &4 \cdot (-1 + 2 - 3 + 4 - 5 + 6 \\ &\qquad {}- 7 + \cdots + 1000)? \end{aligned}$

$-10$

$0$

$1$

$500$

$2000$

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在括号内，将相邻项配对： $\begin{aligned} &(-1+2)+(-3+4) \\ &\quad {}+\cdots+(-999+1000). \end{aligned}$

每一对的和都是 $1$ ，共有 $500$ 对，所以括号内的值是 $500$ 。再乘以 $4$ ，得到 $2000$ 。

所以正确答案是 E。

Within the parentheses, pair consecutive terms: $\begin{aligned} &(-1+2)+(-3+4) \\ &\quad {}+\cdots+(-999+1000). \end{aligned}$

Each pair has sum $1$ , and there are $500$ pairs, so the value inside the parentheses is $500$ . Multiplying by $4$ gives $2000$ .

Thus, E is the correct answer.