(1+1/2+1/3)×(1/2+1/3+1/4)-(1+1/2+1/3+1/4

题库2022-08-02  5

问题 (1+1/2+1/3)×(1/2+1/3+1/4)-(1+1/2+1/3+1/4)×(1/2+1/3)=()A. 1/2B. 1/3C. 1/4D. 1/5

选项 A. 1/2
B. 1/3
C. 1/4
D. 1/5

答案 C

解析 (1+1/2+1/3)×(1/2+1/3+1/4)=(1+1/2+1/3+1/4—1/4) ×(1/2+1/3+1/4) =(1+1/2+1/3+1/4)×(1/2+1/3)+(1+1/2+1/3+1/4)×(1/4)—(1/4) ×(1/2+1/3+1/4)=(1+1/2+1/3+1/4)×(1/2+1/3)+1/4,因此(1+1/2+1/3)×(1/2+1/3+1/4)—(1+1/2+1/3+1/4)×(1/2+1/3)=1/4。故答案为C。
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