You could probably make this truly dynamic with VBA, but I think that's overkill for simply adding a formula to a cell. What you could do is make it appear like the cell is empty until data is added to the pertinent cells, then drag that cell down for hundreds or thousands of rows.
=IF(LEN(A1)=0,"",A1+B1) will show an empty cell if A1 contains no data but will execute the A1+B1 function if it does. If you drag that down below your final row, the column will appear blank until data is added to the next cell in column A.
There are several other formulas you could use to check for cells in use, such as
=ISTEXT(A1) based on how you want to check for data. I think the LEN function easiest to work with. You can also do things like this
=IF(LEN(A1)+LEN(B1)=0,"",A1+B1) which will run the formula if either cell has data, or
=IF(OR(LEN(A1)=0,LEN(B1)=0),"",A1+B1) which will only run the formula if both cells have data.
For most formulas, extending this for several thousand rows only adds a few KB to the size of your file. If you have very lengthy formulas, or many of them, that you are dragging down, it can significantly increase the size of the file.