(1/50-1)(1/49-1)(1/48-1).......(1/4-1)(1/3-1)(1/2-1)
= (-1)^49 * (1-1/50)(1-1/49)...(1-1/2)
= (-1) * (49/50)(48/49)...(2/3)(1/2)
= (-1) * (49*48*............*2*1)/(50*49*48*................*3*2)
= (-1) * (1)/(50)
= -1/50