(1/2010-1)x(1/2009-1)x...x(1/100)-1)
=(-1)^(2010-100+1)(1-1/2010)(1-1/2009).(1-1/100)
=-1*2009/2010*2008/2009*...*99/100
=-99/2009
(1/2010-1)x(1/2009-1)x...x(1/100)-1)
=(-1)^(2010-100+1)(1-1/2010)(1-1/2009).(1-1/100)
=-1*2009/2010*2008/2009*...*99/100
=-99/2009