1x2/1+2x3/1+3x4/1+4x5/1+5x6/1+6x7/1+7x8/1+8x9/1+9x...

1x2/1+2x3/1+3x4/1+4x5/1+5x6/1+6x7/1+7x8/1+8x9/1 =1x2+2x3+3x4+4x5+5x6+6x7+7x8+8x9 =2+6+12+20+30+42+56+72 =20+50+170 =70+170 =240

一千二百六十分之五千五百五十三

原式=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 =4/10 =2/5

1/1X2+1/2X3+1/3X4+1/4X5+1/5X6+1/6X7 =1-1/2+1/2-1/3+1/3-1/4+.+1/6-1/7=1-1/7=6/7;新问题请重新发帖提问,

1/1x2= 1-1/21/2x3=1/2-1/3依此类推原式 = 1-1/2+1/2-1/3+1/3-+1/19-1/20=1-1/20 =19/20

原式=(1-1/2)+(1/2-1/3)+(1/3-1/4)++(1/8-1/9)=1-1/9=8/9

1/1x2+1/2x3+1/3x4+1/4x5+1/5x6+1/6x7=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)=1-1/7=6/71/2+1/6+1/12+1/20+.+1/420=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)

1/1X2+1/2X3+1/3X4+1/4X5+1/5X6……1/2007X2008=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+……+1/2007-1/2008=1-1/2008=2007/2008

公式给你 设N是X的个数x(x+1)=1/(n+1) [x(x+1)(x+2)-(x-1)x(x+1)](1)1x2+2x3+3x4+4x5+5x6+……+10x11=1/3(1*2*3-0*1*2)+1/3(2*3*4-1*2*3)+.1/3(10*11*12-9*10*11)=1/3(1*2*3-0*1*2+2*3*4-1*2*3+.10*11*12-9*10*11)=1

1x2+2x3+3x4+4x5+5x6+6x7+7x8+8x9+9x10+10x11=10*(10+1)*(10+2)÷3=10*11*12÷3=110*12÷3=1320÷3=440

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