学帮网(1-1/2²)×(1-1/3²)×(1-1/4²)…(1-1/2007²)×(1-1/2008²)
来源：学生作业学帮网 编辑：学帮网 时间：2024/05/21 02:36:22
(1-1/2²)×(1-1/3²)×(1-1/4²)…(1-1/2007²)×(1-1/2008²)
(1-1/2²)×(1-1/3²)×(1-1/4²)…(1-1/2007²)×(1-1/2008²)
=((1-1/2)×(1-1/3)×(1-1/4)×…×(1-1/2007)×(1-1/2008))×((1+1/2)×(1+1/3)×(1+1/4)×…×(1+1/2007)×(1+1/2008))
=(1/2×2/3×3/4…2006/2007×2007/2008)×(3/2×4/3×5/4…2008/2007×2009/2008)
=(1/2008)×(2009/2)
=2009/4016