作业帮数学题(1-1/2×1/2)×(1-1/3×1/3)×(1-1/4×1/4)×.×(1-1/2003×1/2003)(1-1/2×1/2)×(1-1/3×1/3)×(1-1/4×1/4)×.×(1-1/2003×1/2003)等于多少
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/14 16:04:44
数学题(1-1/2×1/2)×(1-1/3×1/3)×(1-1/4×1/4)×.×(1-1/2003×1/2003)(1-1/2×1/2)×(1-1/3×1/3)×(1-1/4×1/4)×.×(1-1/2003×1/2003)等于多少
数学题(1-1/2×1/2)×(1-1/3×1/3)×(1-1/4×1/4)×.×(1-1/2003×1/2003)
(1-1/2×1/2)×(1-1/3×1/3)×(1-1/4×1/4)×.×(1-1/2003×1/2003)等于多少
数学题(1-1/2×1/2)×(1-1/3×1/3)×(1-1/4×1/4)×.×(1-1/2003×1/2003)(1-1/2×1/2)×(1-1/3×1/3)×(1-1/4×1/4)×.×(1-1/2003×1/2003)等于多少
(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
(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)×(1-1/4)(1+1/4)×.......×(1-1/2003)(1+1/2003)
=1/2×3/2×2/3×4/3×3/4×5/4……×2002/2003×2004/2003
＝1/2×2004/2003
＝1002/2003