题目

6分之1减15分之1加12分之1减35分之1加20分之1减63分之1用简便运算

提问时间：2021-01-03

答案

1/6-1/15+1/12-1/35+1/20-1/63
=(1/6+1/12+1/20)-(1/15+1/35+1/63)
=[(1/2-1/3)+(1/3-1/4)+(1/4-1/5)]-[1/2×(1/3-1/5)+1/2×(1/5-1/7)+1/2×(1/7-1/9)]
=(1/2-1/3+1/3-1/4+1/4-1/5)-1/2×(1/3-1/5+1/5-1/7+1/7-1/9)
=(1/2-1/5)-1/2×(1/3-1/9)
=3/10-1/2×2/9
=3/10-1/9
=27/90-10/90
=17/90