1/2+1/2×3+1/3×4+……+1/2012×2013

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1/2+1/2×3+1/3×4+……+1/2012×20131/2+1/2×3+1/3×4+……+1/2012×20131/2+1/2×3+1/3×4+……+1/2012×20131/2X3=1/2-

1/2+1/2×3+1/3×4+……+1/2012×2013
1/2+1/2×3+1/3×4+……+1/2012×2013

1/2+1/2×3+1/3×4+……+1/2012×2013

1/2X3=1/2-1/3,同样的,1/3X4=1/3-1/4,以此类推,有
原式=1/2+1/2-1/3+1/3-1/4+.......+1/2012-1/2013
=1-1/2013
=2012/2013