计算:(1-1/2²)(1-1/3²)(1-1/4²)……(1-1/2010²)(1-1/2011²)
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计算:(1-1/2²)(1-1/3²)(1-1/4²)……(1-1/2010²)(1-1/2011²)
计算:(1-1/2²)(1-1/3²)(1-1/4²)……(1-1/2010²)(1-1/2011²)
计算:(1-1/2²)(1-1/3²)(1-1/4²)……(1-1/2010²)(1-1/2011²)
(1-1/2²)(1-1/3²)(1-1/4²)……(1-1/2010²)(1-1/2011²)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)*.(1-1/2010)(1+1/2010)(1-1/2011)(1+1/2011)
=1/2*3/2*2/3*4/3*3/4*5/4*.2009/2010*2011/2010*2010/2011*2012/2011
=1/2*2012/2011
=1006/2011