(1/2009-1)*(1/2008-1)*(1/2007-1)*.*(1/3-1)*(1/2-1)等于多少,

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(1/2009-1)*(1/2008-1)*(1/2007-1)*.*(1/3-1)*(1/2-1)等于多少,
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(1/2009-1)*(1/2008-1)*(1/2007-1)*.*(1/3-1)*(1/2-1)等于多少,
(1/2009-1)*(1/2008-1)*(1/2007-1)*.*(1/3-1)*(1/2-1)等于多少,

(1/2009-1)*(1/2008-1)*(1/2007-1)*.*(1/3-1)*(1/2-1)等于多少,
1/2009 (共有2008个-1相乘,所以结果为正值)

(1/2009-1)*(1/2008-1)*(1/2007-1)*..........*(1/3-1)*(1/2-1)
=(-2008/2009)*(-2007/2008)*(-2006/2007)*...*(-2/3)*(-1/2)
=(-1)^2008 *(1/2009)
=1/2009

1/2009-1)*(1/2008-1)*(1/2007-1)*……*(1/1000-1)
=(-2008/2009)(-2007/2008).....(-999/1000)
因为共有 2008-999+1等于偶数个
所以原式=999/2009