(-1乘2/1)+(-2/1乘3/1)+(-3/1乘4/1)+···+(-2008/1乘2009/1)

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(-1乘2/1)+(-2/1乘3/1)+(-3/1乘4/1)+···+(-2008/1乘2009/1)
(-1乘2/1)+(-2/1乘3/1)+(-3/1乘4/1)+···+(-2008/1乘2009/1)

(-1乘2/1)+(-2/1乘3/1)+(-3/1乘4/1)+···+(-2008/1乘2009/1)
以下*代表乘号
=-(1*2/1+2*3/1+……+2008*2009/1)
=-(1-2/1+2/1-3/1+……+2008/1-2009/1)
=-(1-2009/1)
=-2009分之2008