(1-1/2²)(1-1/3²)×……×(1-1/2011²)(1-1/2012²)
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)x...x(1+1/2011)(1-1/2011)(1+1/2012)(1-1/2012)
=3/2x1/2x4/3x2/3x...2012/2011x2010/2011x2013/2012x2011/2012
=1/2x2013/2012
=2013/4024
(1-1/2²)(1-1/3²)×……×(1-1/2011²)(1-1/2012²)
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)x...x(1+1/2011)(1-1/2011)(1+1/2012)(1-1/2012)
=3/2x1/2x4/3x2/3x...2012/2011x2010/2011x2013/2012x2011/2012
=1/2x2013/2012
=2013/4024