2x4分之1+4x6分之1+6x8分之1.+2012x2014分之一
=1/2x(1/2-1/4)+1/2(1/4-1/6)+...+1/2(1/2012-1/2014)
=1/2x(1/2-1/4+1/4-1/6+.+1/2012-1/2014)
=1/2x(1/2-1/2014)
=1/2x1006/2014
=503/2014