(1/2012-1)*(1/2011-1)*(1/2010-1)*⋯*(1/1000-1)=
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![(1/2012-1)*(1/2011-1)*(1/2010-1)*⋯*(1/1000-1)=](/uploads/image/z/1154314-10-4.jpg?t=%281%2F2012-1%29%2A%281%2F2011-1%29%2A%281%2F2010-1%29%2A%26%238943%3B%2A%281%2F1000-1%29%3D)
(1/2012-1)*(1/2011-1)*(1/2010-1)*⋯*(1/1000-1)=
(1/2012-1)*(1/2011-1)*(1/2010-1)*⋯*(1/1000-1)=
(1/2012-1)*(1/2011-1)*(1/2010-1)*⋯*(1/1000-1)=
(1/2012-1)*(1/2011-1)*(1/2010-1)*⋯*(1/1000-1)
=(-2011/2012)*(-2010/2011)*(-2009/2010)*.*(-999/1000)
=-999/2012
原式=2011/2012 *2010/2011 *2009/2010 *....*1000/1001* 999/1000【约分,分子剩下999,分母剩下2012】
=999/2012
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