1/1*2*3+1/2*3*4+1/3*4*5+.+1/48*49*50 =（1/1*2-1/2*3+1/2*3-1/3*4+1/3*4-1/4*5+……+1/48*19-1/49*50）÷2=（1/1*2-1/49*50）÷2=（1/2-1/2450）÷2=1/4-1/4900=1224/4900=306/1225