(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:作业帮 时间:2024/07/06 12:29:21
![(1-1/2×1/2)×(1-1/3×1/3)×(1-1/4×1/4)×…×(1-1/2005×1/2005)](/uploads/image/z/13304333-29-3.jpg?t=%281-1%2F2%C3%971%2F2%29%C3%97%281-1%2F3%C3%971%2F3%29%C3%97%281-1%2F4%C3%971%2F4%29%C3%97%E2%80%A6%C3%97%281-1%2F2005%C3%971%2F2005%29)
(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