2x4分之1+4x6分之1……2010x2012分之1
=1/4(1/1*2+1/2*3+...+1/1005*1006)
=1/4(1-1/2+1/2-1/3+...+1/1005-1/1006)
=1/4(1-1/1006)
=1005/4024