原式=1/2*(1/1*2-1/2*3)+1/2*(1/2*3-1/3*4)+……+1/2*(1/48*49-1/49*50)
=1/2*(1/1*2-1/2*3+1/2*3-1/3*4+……+1/48*49-1/49*50)
=1/2*(1/1*2-1/49*50)
=306/1225