乘积(1-二的²分之1)(1-三的²分之1)···(1-2010²分之1)(1-2011²分之一)等于
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![乘积(1-二的²分之1)(1-三的²分之1)···(1-2010²分之1)(1-2011²分之一)等于](/uploads/image/z/3651230-38-0.jpg?t=%E4%B9%98%E7%A7%AF%281-%E4%BA%8C%E7%9A%84%26%23178%3B%E5%88%86%E4%B9%8B1%EF%BC%89%281-%E4%B8%89%E7%9A%84%26%23178%3B%E5%88%86%E4%B9%8B1%EF%BC%89%C2%B7%C2%B7%C2%B7%EF%BC%881-2010%26%23178%3B%E5%88%86%E4%B9%8B1%EF%BC%89%EF%BC%881-2011%26%23178%3B%E5%88%86%E4%B9%8B%E4%B8%80%EF%BC%89%E7%AD%89%E4%BA%8E)
乘积(1-二的²分之1)(1-三的²分之1)···(1-2010²分之1)(1-2011²分之一)等于
乘积(1-二的²分之1)(1-三的²分之1)···(1-2010²分之1)(1-2011²分之一)等于
乘积(1-二的²分之1)(1-三的²分之1)···(1-2010²分之1)(1-2011²分之一)等于
(1-二的²分之1)(1-三的²分之1)···(1-2010²分之1)(1-2011²分之一)
=(1+1/2)(1-1/2)(1+1/3)(1-1/3).(1+1/2010)(1-1/2010)(1+1/2011)(1-1/2011)
=(1+1/2)(1+1/3).(1+1/2010)(1+1/2011)(1-1/2)(1-1/3).(1-1/2010)(1-1/2011)
=(3/2)(4/3)...(2011/2010)(2012/2011)(1/2)(2/3)...(2009/2010)(2010/2011)
=(2012/2)(1/2011)
=1006/2011