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10x11+1

原式=(1/10-1/11)+(1/11-1/12)+.....+(1/18-1/19)+(1/19-1/20) =1/10-1/11+1/11-1/12+.....+1/18- 1/19+1/19-1/20 =1/10-1/20 =1/20

算起来有难度

=100/10=10

11/10X11/10X11/10-11/10X11/10-11/10X1/10 =11/10X11/10X(11/10-1-1) =121/100X(-9/10) =-1089/1000

很简单,1∕[a+(a+1)]=1∕a-1∕a+1 代入就得1∕10-1∕100=9∕100

10×11分之1+11×12分之1+12×13分之1+............+59×60分之1 =(10分之1-11分之1)+(11分之1-12分之1)+(12分之1-13分之1)+……+(59分之1-60分之1) =10分之1-11分之1+11分之1-12分之1+12分之1-13分之1+……+59分之1-60分之1 ...

1+11x111-1111 = 1 + (10 + 1) x 111 - (1000 + 111) = 1 + 1110 + 111 - 1000 - 111 = 1 + 110 = 111

1x2+2x3+3x4+…+n(n+1) =1x(1+1)+2x(2+1)+3x(3+1)+…n(n+1) =(1^2+2^2+3^2+…+n^2)+(1+2+3+…+n) =n(n+1)(2n+1)/6+n(n+1)/2 =n(n+1)[(2n+1)+3]/6 1x2+2x3+3x4+…+10x11 =10x(10+1)x[(10x2+1)+3]/6 =110x4 =440

解:①2x3/1+3x4/1+4x5/1+5x6/1+6x7/1+7x8/1+8x9/1+9x10/1+10x11/1 =6+12+20+30+42+56+72+90+110 =(6+12+72)+(20+30+90+110)+(42+56) =90+250+98 =438 ②如果楼主原意这样,那么解法不同: 1/2x3+1/3x4+1/4x5+1/5x6+1/6x7+1/7x8+1/8x9+1/9x10+1/10...

10.68x11-1.68 =10.68x10 + 10.68-1.68 =106.8 + 9 =115.8

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