计算(1-1/2²)(1-1/3²).(1-1/2012²)(1-1/2013²)
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计算(1-1/2²)(1-1/3²).(1-1/2012²)(1-1/2013²)
计算(1-1/2²)(1-1/3²).(1-1/2012²)(1-1/2013²)
计算(1-1/2²)(1-1/3²).(1-1/2012²)(1-1/2013²)
答:
(1-1/2²)(1-1/3²).(1-1/2012²)(1-1/2013²)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3).(1-1/2012)(1+1/2012)(1-1/2013)(1+1/2013)
=(1/2)*(3/2)*(2/3)*(4/3).(2011/2012)*(2013/2012)*(2012/2013)*(2014/2014)
=(1/2)*(2014/2013)
=1007/2013