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问题: 简便运算

1/20+1/30+1/42+1/56

解答:

1/20=1/(4*5)=(1/4)-(1/5)
1/30=1/(5*6)=(1/5)-(1/6)
1/42=1/(6*7)=(1/6)-(1/7)
1/56=1/(7*8)=(1/7)-(1/8)
原式=(1/4)-(1/5)+(1/5)-(1/6)+(1/6)-(1/7)+(1/7)-(1/8)=(1/4)-(1/8)=1/8