计算：（1-1/2^2）*(1-1/3^2)*(1-1/4^2)*.*(1-1/2011^2)*(1-1/2012^2)

（1-1/2^2）*(1-1/3^2)*(1-1/4^2)*.*(1-1/2011^2)*(1-1/2012^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4).(1-1/2011)(1+1/2011)(1-1/2012)(1+1/2012)
=1/2*3/2*2/3*4/3*3/4*5/4*.*2010/2011*2012/2011*2011/2012*2013/2012
=1/2*2013/2012
=2013/4024

（1-1/2^2）(1-1/3^2)(1-1/4^2).......(1-1/2009^2)(1-1/2010^2).
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)……(1-1/2009)(1+1/2009)(1-1/2010)(1+1/2010)
=(1/2)(3/2)(2/3)(4/3)(3/4)(5/4)……(2008/2009)(2...

（1-1/2^2）*(1-1/3^2)*(1-1/4^2)*.......*(1-1/2011^2)*(1-1/2012^2)
=（1+1/2）（1-1/2)（1+1/3）(1-1/3)（1+1/4）(1-1/4)×……×（1+1/2011）×（1-1/2011）×（1+1/2012）(1-1/2012)
=3/2×4/3×5/4×……×2012/2100×2013/2011×1/2×2/3×3/4×……×2010/2011×2011/2012
=2013/2×1/2012
=2013/4024