(1-2²/1)×(1-3²/1)×...(1-2004²/1)×(1-2005²/1)
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/23 23:47:57
![(1-2²/1)×(1-3²/1)×...(1-2004²/1)×(1-2005²/1)](/uploads/image/z/169761-57-1.jpg?t=%281-2%26%23178%3B%2F1%29%C3%97%281-3%26%23178%3B%2F1%29%C3%97...%281-2004%26%23178%3B%2F1%29%C3%97%281-2005%26%23178%3B%2F1%29)
(1-2²/1)×(1-3²/1)×...(1-2004²/1)×(1-2005²/1)
(1-2²/1)×(1-3²/1)×...(1-2004²/1)×(1-2005²/1)
(1-2²/1)×(1-3²/1)×...(1-2004²/1)×(1-2005²/1)
平方差
(1-2²/1)×(1-3²/1)×...(1-2004²/1)×(1-2005²/1)
=(1-2/1)×(1+2/1)×(1-3/1)×(1+3/1)...(1-2005/1)×(1+2005/1)
=2/1×2/3×3/2×3/4……2005/2004×2005/2006
中间约分
=2/1×2005/2006
=2005/1003