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: 2, 5, ['r', 'Y', '3769', 'k', '6407', 'G', 'M']
Example Output: 10176

Example Input: 5, 9, ['r', 'P', 'r', 'g', '5077', 'T', '2819', 'f', 'p', '6449', '8509', '8915', 'I', 'Z', 'N', '8657', 'R', '3739']
Example Output: 7896

Example Input: 5, 12, ['s', '1987', '6175', 'T', 'I', '2507', 'Y', '175', 's', '5479', 'i', '6559', 'f', '6411', '7869', 'f']
Example Output:
14720