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1/2X4+1/4X6+1/6X8+1/8X10+1/10X12=

1/2X4+1/4X6+1/6X8+1/8X10+1/10X12=(1/2-1/4+1/4-1/6+1/6-1/8+1/8-1/10+1/10-1/12)÷2=(1/2-1/12)÷2=5/12÷2=5/24

因为1/[n(n+2)]=1/2*[1/n-1/(n+2)]所以1/4x1/6+1/6x1/8+1/8x1/10+1/10x1/12=1/2*(1/4-1/6+1/6-1/8+1/8-1/10+1/10-1/12)=1/2*(1/4-1/12)=1/12所以(1/4x1/6+1/6x1/8+1/8x1/10+1/10x1/12)x2=1/12*2=1/6

1/2x4+1/4x6+1/6x8+1/8x10+..1/1996x1998=1/4(1/1*2+1/2*3+1/3*4+……+1/998*999)=1/4(1-1/2+1/2-1/3+1/3-1/4+……+1/998-1/999)=1/4(1-1/999)=499/1998

1/2x4+1/4x6+1/6x8+1/8x10+.1/1996x1998=1/4(1/1*2+1/2*3+1/3*4+……+1/998*999)=1/4(1-1/2+1/2-1/3+1/3-1/4+……+1/998-1/999)=1/4(1-1/999)=499/1998

1/2x4+1/4x6+1/6x8+……+1/98x100=1/2{(1/2-1/4)+(1/4-1/6)+(1/6-1/8)+[1/(2x50-2)-1/2x50]} =1/2*(1/2-1/2x50) =1/4-1/(4x50) =49/200 9/5,16/12,25/21,36/32,观察可得,分子总比分母大四,分子为(n+2)^2 所以第9个为(9+2)^2/(11^2-4)=121/117

1/2x4+1/4x6+1/6x8+..+1/2010x2012=1/2[(1/2-1/4)+(1/4-1/6)+(1/6-1/8)+[1/2010-1/2012] =1/2*(1/2-1/2012) =1/2*1005/2012=1005/4024

我觉得你想表达的意思和你打的不一样,错了不要怪我. 1/(2*4)可以看成1/2*(1/2-1/4),把每项都拆开,前后抵消,易得结果为1/2*(1/2-1/50)=12/50

原式=1/2x(2/2x4+2/4x6+2/6x8++2/2012x2014)=1/2x(1/2-1/4+1/4-1/6+1/6-1/8++1/2012-1/2014)=1/2x(1/2-1/2014)=1/2x1006/2014=1003/2014

8+24+48+120=200、这是最简单的

原式=0.5*(1/2-1/4+1/4-16++1/48-1/50)=0.5*(1/2-1/50)=6/25

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