(1/1009-1)*(1/1010-1)*.*(1/20009-1)*(1/2010-1)

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(1/1009-1)*(1/1010-1)*.*(1/20009-1)*(1/2010-1)
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(1/1009-1)*(1/1010-1)*.*(1/20009-1)*(1/2010-1)
(1/1009-1)*(1/1010-1)*.*(1/20009-1)*(1/2010-1)

(1/1009-1)*(1/1010-1)*.*(1/20009-1)*(1/2010-1)
(1/1009-1)*(1/1010-1)*.*(1/2009-1)*(1/2010-1)
=(-1008/1009)*(-1009/1010)*……*(-2008/2009)*(-2009/2010)
=(-1)^1002*1008/2010
=1008/2010