(1-1/1006^2)(1-1/1007^2)(1-1/1008^2)……(1-1/2011^2)怎么做?
来源：学生作业帮助网 编辑：六六作业网 时间：2024/12/19 07:41:03
(1-1/1006^2)(1-1/1007^2)(1-1/1008^2)……(1-1/2011^2)怎么做?
(1-1/1006^2)(1-1/1007^2)(1-1/1008^2)……(1-1/2011^2)怎么做?
(1-1/1006^2)(1-1/1007^2)(1-1/1008^2)……(1-1/2011^2)怎么做?
=(1-1/1006)(1+1/1006)(1-1/1007)(1+1/1007)(1-1/1008)(1+1/1008)……(1-1/2011)(1+1/2011)
=1005/1006 × 1007/1006×1006/1007 × 1008/1007×1007/1008 × …… ×2011/2010×2010/2011 ×2012/2011
=1005/1006 ×2012/2011
=2010/2011
等于2010/2011
=(1-1/1006)(1+1/1006)(1-1/1007)(1+1/1007)(1-1/1008)(1+1/1008)……(1-1/2011)(1+1/2011)
=1005/1006 × 1007/1006×1006/1007 × 1008/1007×1007/1008 × …… ×2011/2010×2010/2011 ×2012/2011
=1005/1006 ×201...
全部展开
=(1-1/1006)(1+1/1006)(1-1/1007)(1+1/1007)(1-1/1008)(1+1/1008)……(1-1/2011)(1+1/2011)
=1005/1006 × 1007/1006×1006/1007 × 1008/1007×1007/1008 × …… ×2011/2010×2010/2011 ×2012/2011
=1005/1006 ×2012/2011
=2010/2011
收起