计算1/1*2*3+1/2*3*4+1/3*4*5+.+1/48*49*50

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