(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)…(1-1/2011)(1+1/2011)
=1/2*3/2*2/3*4/3*3/4*5/4…2011/2010*2010/2011*2012/2011
=1/2*(3/2*2/3)*(4/3*3/4)*5/4…(2011/2010*2010/2011)*2012/2011
=1/2*2012/2011
=1006/2011