Sum Everything Upto The Current Row Number

So, I need to keep adding together all the numbers from cell row 0 upto and including the row number of the cell with the result. The column with the results is to the right of the column with numbers to add. So, if the numbers are positive, to the right of each should be an ever increasing number as a result. In the column with the numbers to add is a function which as a result gives either numbers or blank cells. It sounds simple but it is frustrating me. Why can't I use the function SUMIF with a ROW function inside the condition field? It always gives me 0 as the result. I use excel 2003.

I probably do't understand the SUMIF function but why isn't =SUMIF(A:A;"1>0") equivalent to =SUM(A:A). This too gives the result of 0. Why don't I get an error instead.