1/2*4+1/4*6+1/6*8+....1/48*50=1/2*(1/2-1/4)+1/2*(1/4-1/6)+1/2*(1/6-1/8)+......+1/2*(1/48-1/50)=1/2*(1/2-1/4+1/4-1/6+1/6-1/8+......+1/48-1/50)=1/2*(1/2-1/50)=1/2*12/25=6/25