(1-1/4)*(1-1/9)*^(1-1/2008²）是多少呀
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(1-1/4)(1-1/9)(1-1/16)...(1-1/2008²)
=(1-1/2²)(1-1/3²)(1-1/4²)...(1-1/2008²)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)...(1-1/2008)(1+1/2008)
=(1/2)(3/2)(2/3)(4/3)(3/4)(5/4)...(2007/2008)(2009/2008)
=(1/2)(2009/2008) (中间都约分约掉了)
=2009/4016
=(1-1/2²)(1-1/3²)(1-1/4²)...(1-1/2008²)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)...(1-1/2008)(1+1/2008)
=(1/2)(3/2)(2/3)(4/3)(3/4)(5/4)...(2007/2008)(2009/2008)
=(1/2)(2009/2008) (中间都约分约掉了)
=2009/4016
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