A family of Microsoft spreadsheet software with tools for analyzing, charting, and communicating data.
This is not an uncommon problem attempting to link formulas to closed workbooks. I usually advise users to do the following and it removes the headaches.
Instead of linking formulas to closed workbooks you will have more success if you copy the data from the source and use PasteSpecial -> Paste Link into a worksheet in the destination workbook. That way you only have all of the cells linked to the source without the formulas. Then set up your formulas to simply reference the linked worksheet. The linked worksheet can be hidden.
Also I would use the following formula with Offset to reference the range to be summed. Note that this formula will not work at all if referencing a closed workbook but works well on a hidden worksheet that is linked to the source. Name of the hidden linked worksheet is "Link to Source". Reason for subtracting 1 from A2 is that offset works on the basis of how many times you would need to press the down arrow to get to the offset cell and so if you enter 4 in cell A2 then if you selected F4 then you would need to press the down arrow 3 times to get to the 4th cell.
=SUM('Link To Source'!F4:OFFSET('Link To Source'!F4,A2-1,0,1,1))
Following added after initial posting.
An even simpler formula. See Help for more information on Offset function. The formula works using the height from the initial cell. Note that A2 does not have 1 subtracted from it (as previous formula) because the height is the total height including the first and last row and there is actually no offset to rows or columns; it is simply the reference for a total height of A2 where the reference is the first cell and the height is total rows down.
=SUM(OFFSET('Link To Source'!F4,0,0,A2,1))