(1-1/2×1/2)×(1-1/3×1/3)×(1-1/4×1/4)×…×(1-1/2005×1/2005)
来源：学生作业帮助网 编辑：六六作业网 时间：2024/07/14 03:57:50
(1-1/2×1/2)×(1-1/3×1/3)×(1-1/4×1/4)×…×(1-1/2005×1/2005)(1-1/2×1/2)×(1-1/3×1/3)×(1-1/4×1/4)×…×(1-1/20
(1-1/2×1/2)×(1-1/3×1/3)×(1-1/4×1/4)×…×(1-1/2005×1/2005)
(1-1/2×1/2)×(1-1/3×1/3)×(1-1/4×1/4)×…×(1-1/2005×1/2005)
(1-1/2×1/2)×(1-1/3×1/3)×(1-1/4×1/4)×…×(1-1/2005×1/2005)
(1-1/2×1/2)×(1-1/3×1/3)×(1-1/4×1/4)×.×(1-1/2003×1/2003)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)……（1-1/2003）（1+1/2003）
=1/2*3/2*2/3*4/3*……*2002/2003*2004/2003
=1/2*2004/2003
=1002/2003