(1-1/2²)(1-1/3²)(1-1/4²)(1-1/5²)……(1-1/2007²)(1-1/2008²)要过程!
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(1-1/2²)(1-1/3²)(1-1/4²)(1-1/5²)……(1-1/2007²)(1-1/2008²)要过程!(1-1/2
(1-1/2²)(1-1/3²)(1-1/4²)(1-1/5²)……(1-1/2007²)(1-1/2008²)要过程!
(1-1/2²)(1-1/3²)(1-1/4²)(1-1/5²)……(1-1/2007²)(1-1/2008²)
要过程!
(1-1/2²)(1-1/3²)(1-1/4²)(1-1/5²)……(1-1/2007²)(1-1/2008²)要过程!
(1-1/2²)(1-1/3²)(1-1/4²)(1-1/5²)……(1-1/2007²)(1-1/2008²)
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)……(1+1/2007)(1-1/2007)(1+1/2008)(1-1/2008)
=(1+1/2)(1+1/3)……(1+1/2008)*(1-1/2)(1-1/3)(1-1/2008)
=3/2*4/3*5/4*……*2009/2008*1/2*2/3*3/4*……*2007/2008
=2009/2*1/2008
=2009/4016
=(1+1/2)*(1-1/2) *(1+1/3)*(1-1/3)--------*(1+1/2007)*(1-1/2007)*(1+1/2008)*(1-1/2008)*
=(1+1/2)*(1+1/3)----*(1+1/2008)*(1-1/2)*(1-1/3)----*(1-1/2008)
=3/2*4/3*5/4---------*2009/2008*1/2*2/3*3/4*-----------2007/2008(分子分母可以消除的)
=2009/2*1/2008(最后结果自己算吧)