计算:(1/2012-1)×(1/2011-1)×(1/2010-1)×(1/2009-1)×...×(1/2011-1)×(1/2000-1)

问题描述:

计算:(1/2012-1)×(1/2011-1)×(1/2010-1)×(1/2009-1)×...×(1/2011-1)×(1/2000-1)

(1/2012-1)x(1/2011-1)x(1/2010-1)x(1/2009-1)x(1/2008-1)x.(1/2001-1)x(1/2000-1)=(-2011/2012)(-2010/2011)*(-2009/2010)...(-2000/2001)(-1999/2000)=1999/2012