(1-1/2²)(1-1/3²)(1-1/4²)……*(1-1/2008²)

(1-1/2²)(1-1/3²)(1-1/4²)……*(1-1/2008²)
(1-1/2²)(1-1/3²)(1-1/4²)……*(1-1/2008²)

(1-1/2²)(1-1/3²)(1-1/4²)……*(1-1/2008²)
(1-1/2²)(1-1/3²)(1-1/4²)……*(1-1/2008²)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)·····(1-1/2008)(1+1/2008)
=1/2x3/2x2/3x4/3x3/4x5/3x···x2007/2008x2009/2008
=1/2x2009/2008
=2009/4016

(1-1/2²)*(1-1/3²)*(1-1/4²)*……*(1-1/2008²)
=(1-1/2)*(1+1/2)*(1-1/3)*(1+1/3)*(1-1/4)*(1+1/4)*……*(1-1/2008)(1+1/2008)
=1/2*3/2*2/3*4/3*3/4*5/4*……*2007/2008*2009/2008
=1/2*（3/2*2/3）*（4/3*3/4）（*5/4*4/5）*……*（2006/2007*2007/2008）*2009/2008
=1/2*2009/2008
=2009/4016