(1-(1/2^2))(1-(1/3^2))(1-(1/4^2))```````(1-(1/100^2))(2008^2-2*2008^2-2006)/(2008^2+2008^2-2009)
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 21:21:29
![(1-(1/2^2))(1-(1/3^2))(1-(1/4^2))```````(1-(1/100^2))(2008^2-2*2008^2-2006)/(2008^2+2008^2-2009)](/uploads/image/z/10215015-15-5.jpg?t=%281-%281%2F2%5E2%29%29%281-%281%2F3%5E2%29%29%281-%281%2F4%5E2%29%29%60%60%60%60%60%60%60%281-%281%2F100%5E2%29%29%EF%BC%882008%5E2-2%2A2008%5E2-2006%EF%BC%89%2F%EF%BC%882008%5E2%2B2008%5E2-2009%EF%BC%89)
(1-(1/2^2))(1-(1/3^2))(1-(1/4^2))```````(1-(1/100^2))(2008^2-2*2008^2-2006)/(2008^2+2008^2-2009)
(1-(1/2^2))(1-(1/3^2))(1-(1/4^2))```````(1-(1/100^2))
(2008^2-2*2008^2-2006)/(2008^2+2008^2-2009)
(1-(1/2^2))(1-(1/3^2))(1-(1/4^2))```````(1-(1/100^2))(2008^2-2*2008^2-2006)/(2008^2+2008^2-2009)
1、
用平方差
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)……(1-1/100)(1+1/100)
=(1/2)(3/2)(2/3)(4/3)……(99/100)(101/100)
=(1/2)(101/100)
=101/200
2、
题目写错了
应该是(2008^3-2*2008^2-2006)/(2008^3+2008^2-2009)
分子=2008^2(2008-2)-2006=2008^2*2006-2006=2006*(2008^2-1)
分母=2008^2(2008+1)-2009=2008^2*2009-2009=2009*(2008^2-1)
所以原式=2006/2009