In this task, you are given inputs i,j, and A, where i and j are integers and A is a list. You need to return the sum of all the numerical elements in the list A between the positions i and j (including positions i and j). Return 0 if no numerical element is present in the list between the given ranges. i and j will be non-negative, and will always have a value less than the length of A. i will always be less than j.

Example Input: 3, 13, ['9585', '4573', '8113', '4163', 'D', '4641', '2077', 'D', '5339', 'Y', 'Z', '9133', '9401', 'o', '5033', 'd', '1745', '1357', '5513', '5369', 'N', '9355', 'C', 'W', 'C']
Example Output: 42867

Example Input: 14, 17, ['Q', '7681', '8379', '2569', 'D', '5179', 'M', 'M', 'k', '187', '9275', 'V', 'L', 'F', '6397', '6385', 'O', '4823', '8655']
Example Output: 12782

Example Input: 1, 6, ['q', 'n', '1225', '9957', '5059', '6763', '9911', '4627', 'O', '9399', 'C', '1917', '565', 'T']
Example Output:
23004