(1- 1/2^2)(1- 1/3^2)(1- 1/4^2)……(1- 1/2007^2)(1- 1/2008^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)……(1-1/2008)(1+1/2008)
=(1/2)(3/2)(3/4)(5/4)……(2007/2008)(2009/2008)
=(1/2)(2009/2008)
=2009/4016
(1- 1/2^2)(1- 1/3^2)(1- 1/4^2)……(1- 1/2007^2)(1- 1/2008^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)……(1-1/2008)(1+1/2008)
=(1/2)(3/2)(3/4)(5/4)……(2007/2008)(2009/2008)
=(1/2)(2009/2008)
=2009/4016