(1-1/2)*(1+1/2)*(1-1/3)*(1+1/3)*(1-1/4)*(1+1/4)*.*(1+1/2004)*(1-1/2004)
问题描述:
(1-1/2)*(1+1/2)*(1-1/3)*(1+1/3)*(1-1/4)*(1+1/4)*.*(1+1/2004)*(1-1/2004)
答
(1-1/2)*(1+1/2)*(1-1/3)*(1+1/3)*(1-1/4)*(1+1/4)*.*(1+1/2004)*(1-1/2004)
=(1/2)*(3/2)*(2/3)*(4/3)*.(2003/2004)*(2005/2004)
=(1/2)*(2005/2004)
=2005/4008