(1/2009-1)*(1/2008-1)*(1/2007-1)*……*(1/3-1)*(1/2-1)
问题描述:
(1/2009-1)*(1/2008-1)*(1/2007-1)*……*(1/3-1)*(1/2-1)
答
一共2008项,乘积为正
(1/2009-1)*(1/2008-1)*(1/2007-1)*……*(1/3-1)*(1/2-1)
=(1-1/2)*(1-1/3)*...*(1-1/2008)*(1-1/2009)
=1/2*2/3*3/4*...*2007/2008*2008/2009
=1/2009