How to simplify the calculation from 1 x 1 / 2 plus 2 times 1 / 3 and so on to 49 times 50

How to simplify the calculation from 1 x 1 / 2 plus 2 times 1 / 3 and so on to 49 times 50


1/1*2+1/2*3+...+1/49*50
=1-1/2+1/2-1/3+...+1/49-1/50
=1-1/50
=49/50



How to calculate 4 times 50 times 60 times 8


=(4×60)×(50×8)
=240×400
=96000