1-1/n^2 = (n-1)/n * (n+1)/n
:(1-1/2^2)(1-1/3^2)…(1-1/2007^2)(1-1/2008^2)
= 1/2*3/2*2/3*4/3*3/4*5/4*...*2006/2007*2008/2007*2007/2008*2009/2008
= 1/2*2009/2008
=2009/4016
1-1/n^2 = (n-1)/n * (n+1)/n
:(1-1/2^2)(1-1/3^2)…(1-1/2007^2)(1-1/2008^2)
= 1/2*3/2*2/3*4/3*3/4*5/4*...*2006/2007*2008/2007*2007/2008*2009/2008
= 1/2*2009/2008
=2009/4016