作业帮(1-1/2²)×(1-1/3²)×(1-1/4²)…(1-1/2007²)×(1-1/2008²)
来源：学生作业帮助网 编辑：作业帮 时间：2024/08/27 11:30:34
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(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)
(1-1/2²)×(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