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: 3, 8, ['g', 'D', 'W', 'q', '7817', '9295', '2385', 'V', 'c', '7761']
Example Output: 19497

Example Input: 4, 15, ['V', 'H', '7121', 'o', '6169', 'Y', 'F', 'e', 'b', '869', 'c', 'e', 'D', '7495', 'B', 'g', '4573', 'e', 'A', '4483', '8919', '3923', 'N']
Example Output:
14533