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: 11, 14, ['H', '4643', 'k', '9583', 'K', '3497', 'Q', '8111', '1837', 'Z', '6885', 'L', '1759', '7777', '3137']
Example Output: 16421

Example Input: 7, 12, ['273', 'h', '2433', '7155', '731', '5459', 'q', 'G', 'i', 'l', '3981', 'W', 'V', '4999', '8191', 'K', '8393', '9255']
Example Output: 3981

Example Input: 8, 9, ['S', '163', 'i', '1013', 'b', '6269', 'k', 'u', '6783', 'b', '3607', 'n']
Example Output:
6783