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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=5/241-5/6+7/12-9/20+11/30=1/6+7/12-9/20+11/30=(1/2-1/3)+(1/3+1/4)-(1/4+1/5)+(1/5+1/6)=1/2+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

8+24+48+120=200、这是最简单的

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++……+1/2k(2k+2)+1/(2k+2)(2k+4)=(1/2)x[2/2x4+2/4x6+……+2/2k(2k+2)+2/(2k+2)(2k+4]=(1/2)x[1/2-1/4+1/4-1/6+……+1/2k-1/(2k+2)+1/(2k+2)-1/(2k+4]中间正负抵消=(1/2)x[1/2-1/(2k+4]=1/4-1/(4k+8)=(k+1)/(4k+8)他的这个答案也对,但是没有化到最简

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

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

2x4分之一+4x6分之一+6x8分之一+98x100分之一=1/2*(1/2-1/4)+1/2*(1/4-1/6)++1/2*(1/98-1/100)=1/2*(1/2-1/4+.+1/98-1/100)=1/2*49/100=49/200;

4X6+1应该等于25 规律是两个连续偶数之积加1等于这两个偶数之间的奇数的平方第N个等式是2n*(2n+2)+1=(2n+1)^2

计算,1/2x4+1/4x6+1/6x8++1/48x50=1/2*(1/2-1/4+1/4-1/6+1/6-1/8+……+1/48-1/50)=1/2*(1/2-1/50)=1/2*12/25=6/25,1/2+1/6+1/12+1/20+1/30+1/42=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=6/7

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