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(1/3-1/4)+(1/4-1/5)+(1/5-1/6) 7×13×(8/7-14/13)

1/3*1/4+1/4*1/5+1/5*1/6+1/6*1/7=1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7=1/3-1/7=4/21

1/2*1/3 1/3*1/4 1/4*1/5 1/5*1/6 1/6*1/7 1/7*1/8 1/8*1/9 1/9*1/10 =1/2-1/3 1/3-1/4 1/4-1/5 1/5-1/6 1/6-1/7 1/7-1/8 1/8-1/9 1/9-1/10 =1/2-1/10 =2/5 结果是五分之二

14/15

1-1/2+1/3-1/4+1/5-1/6+1/7-1/8+1/9-1/10 =(1-1/2-1/4-1/8)+(1/3-1/6+1/9)+(1/5-1/10)+1/7=1/8+5/18+1/5+1/7=13/40+53/126=1879/2520

1/1*3+1/2*4+1/3*5+1/4*6+1/5*7+1/6*8+1/7*9+1/8*10+1/9*11 =(1/2)*[(1-1/3)+(1/2-1/4)+(1/3-1/5)+(1/4-1/6)+(1/5-1/7)+(1/6-1/8)+(1/7-1/9)+(1/8-1/10)+(1/9-1/11)] =(1/2)*[(1-1/11)+(1/2-1/10)] =(1/2)*(10/11+2/5) =5/11+1/5=36/55.

3*4*5*6*7*8*9=181440

(1+1\3)*(1+1\5)*(1+1\7)**(1+1\17)*(1-1/4)*(1-1/6)*(1-1/8)**(1-1/18)=4/3*6/5*8/7**18/17*3/4*5/6*7/8**17/18=4/3*3/4*6/5*5/6*8/7*7/8**18/17*17/18=1

解:1/2-1/3+1/4-1/5+1/6-1/7+1/8-1/9+1/10 =(1/2-1/3)+(1/4-1/5)+(1/6-1/7)+(1/8-1/9)+1/10 =1/(2*3)+1/(4*5)+1/(6*7)+1/(8*9)+1/10 =1/6+1/20+1/42+1/72+1/10 =893/2520

(1/3+1/4+1/5+1/6)*(1/4+1/5+1/6+1/7)-(1/3+1/4+1/5+1/6+1/7)*(1/4+1/5+1/6) ={(1/4+1/5+1/6)*(1/4+1/5+1/6+1/7)+1/3*(1/4+1/5+1/6+1/7)}-{(1/4+1/5+1/6+1/7)*(1/4+1/5+1/6)+1/3*(1/4+1/5+1/6)} =1/3*1/7 =1/21

(1/3-2/1)/(1/4+1/3)*(-1/5-1/4)/(1/6+1/5)*(1/7-1/6)/(-1/8+1/7)=-1/6/(5/12)*(-9/20)/(11/30)*(-1/42)/(1/56)=-2/5*(-9/20)*30/11*(-1/42)*56=9/50*30/11*(-8/7)=9/55*(-8/7)=-72/3

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