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乘积(1-1/2^2)(1-1/3^2)(1-1/4^2).(1-1/2009^2)(1-1/2010^2)(1-1/2

来源:学生作业帮 编辑:作业帮 分类:综合作业 时间:2024/05/26 23:58:52
乘积(1-1/2^2)(1-1/3^2)(1-1/4^2).(1-1/2009^2)(1-1/2010^2)(1-1/2011^2)=_____?
请注意格式,
乘积(1-1/2^2)(1-1/3^2)(1-1/4^2).(1-1/2009^2)(1-1/2010^2)(1-1/2011^2)
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)(1+1/4)(1-1/4)...(1+1/2009)(1-1/2009)(1+1/2010)(1-1/2010)(1+1/2011)(1-1/2011)
=(3/2)(1/2)(2/3)(4/3)(5/4)(3/4)...(2010/2009)(2008/2009)(2011/2010)(2009/2010)(2012/2011)(2010/2011)
=(1/2)(3/2)(2/3)(4/3)(3/4)(5/4)...(2008/2009)(2010/2009)(2009/2010)(2011/2010)(2010/2011)
(2012/2011)
=(1/2)(2012/2011)
=1006/2011