(1-1/2^2)(1-1/3^2)(1-1/4^2)…(1-1/2008^2)(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)......(1-1/2008)*(1+1/2008)*(1-1/2009)*(1+1/2009) *(1-1/2010)*(1+1/2010)
=1/2 * 3/2 * 2/3 * 4/3 * 5/4......2007/2008 * 2008/2009 * 2010/2009
=1/2 * 2010/2009 *2011/2010
=1/2*2011/2009
=2011/4018