Where G has a direction and H has a direction.

The gravity direction is downward, and the downward direction is selected as the positive direction.

Then the rise of H, the displacement is -H, and the work done by gravity is -—mgh.

Descending h, displacement h and gravity work mgh.

So the total work done by gravity w =-mgh+mgh = o.

Who taught you that?

This is calculus. I just learned it in college, and I also said some math in Grade Two.

Actually, it's exactly what I said.

But there is something wrong with your supplement. Not that the cumulative force is O, but that the cumulative displacement is zero.

H in mgh is the displacement. When it returns to its original position, the displacement H is zero and the work done by gravity is zero.