Question

求表达式的值。 $\begin{gathered} 100 - 98 + 96 - 94 + 92 - 90 \\ {}+ \cdots + 8 - 6 + 4 - 2. \end{gathered}$

Find the value of the expression $\begin{gathered} 100 - 98 + 96 - 94 + 92 - 90 \\ {}+ \cdots + 8 - 6 + 4 - 2. \end{gathered}$

$20$

$40$

$50$

$80$

$100$

答案：C

知识点：配对与分组

难度评级：900

视频讲解：

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文字解答：

可以把和分组为每一对的值都是 $2$ ，共有 $25$ 对。因此总和为 $2 \cdot 25 = 50$ 。 $\begin{gathered} (100 - 98) + (96 - 94) \\ {}+ \cdots + (4 - 2). \end{gathered}$

所以正确答案是 C。

We can group the sum as follows: $\begin{gathered} (100 - 98) + (96 - 94) \\ {}+ \cdots + (4 - 2). \end{gathered}$ Note that each pair evaluates to $2$ and there are $25$ pairs. Therefore, the total sum is $2 \cdot 25 = 50.$

Thus, C is the correct answer.

2016 AMC 8 第 8 题

答案：C

难度评级：900

视频讲解：

文字解答：

其他年份的第 8 题