1/1X2X3+1/2X3x4+…+1/48X49X50
=（1/1X2-1/2X3+1/2X3-1/3x4+…+1/48X49-1/49X50）÷2
= （1/1X2-1/49X50）÷2
=（1/2-1/2450）÷2
=1224/2450÷2
=306/1225