(1-1/2)*(1/3-1)*(1-1/4)*(1/5-1)...(1-2008)*(1/2009-1)

问题描述:

(1-1/2)*(1/3-1)*(1-1/4)*(1/5-1)...(1-2008)*(1/2009-1)

(1-1/2)*(1/3-1)*(1-1/4)*(1/5-1)...(1/2008-1)*(1/2009-1)
=(-1/2)*(-2/3)*(-3/4)*(-4/5)*……*(-2007/2008)*(-2008/2009)
=1/2009