1/1x2=1-1/2,1/2x3=1/2-1/3,1/3x4=1/3-1/4.那么1/2x4+1/4x6+1/6x8.1/2006x2007=?

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1/1x2=1-1/2,1/2x3=1/2-1/3,1/3x4=1/3-1/4.那么1/2x4+1/4x6+1/6x8.1/2006x2007=?
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1/1x2=1-1/2,1/2x3=1/2-1/3,1/3x4=1/3-1/4.那么1/2x4+1/4x6+1/6x8.1/2006x2007=?
1/1x2=1-1/2,1/2x3=1/2-1/3,1/3x4=1/3-1/4.那么1/2x4+1/4x6+1/6x8.1/2006x2007=?

1/1x2=1-1/2,1/2x3=1/2-1/3,1/3x4=1/3-1/4.那么1/2x4+1/4x6+1/6x8.1/2006x2007=?
=1/2*(1/2-1/4+1/4-1/6+1/6-1/8+……+1/2004-1/2006)+1/2006-1/2007
=1/2*(1/2-1/2006)+1/2006-1/2007
=1/4+1/4012-1/2007
=502754/2013021
=0.24975

笨，没找到规律！这是哪里的题？