AMC8 2016

AMC8 2016 · Q8

AMC8 2016 · Q8. It mainly tests Arithmetic sequences basics, Arithmetic misc.

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

求表达式的值：$100 - 98 + 96 - 94 + 92 - 90 + \cdots + 8 - 6 + 4 - 2$。

(A) 20 20

(B) 40 40

(D) 80 80

(E) 100 100

Answer

Correct choice: (C)

正确答案：（C）

Solution

Evaluate the expression by grouping as follows: $(100-98)+(96-94)+\cdots+(8-6)+(4-2)=2+2+\cdots+2+2=2\cdot25=50$.

按如下方式分组计算该表达式：$(100-98)+(96-94)+\cdots+(8-6)+(4-2)=2+2+\cdots+2+2=2\cdot25=50$。

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