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: 8, 9, ['3587', '5903', 'B', '9671', 's', 'A', '7259', '6961', '2601', '9719']
Example Output: 9562

Example Input: 3, 4, ['2977', 'i', 'l', 'r', '8835', '7697', 'p', '1685', 'h', 'N', 'Z', '8661', '6003', '7007', 'D', 'C']
Example Output: 0

Example Input: 4, 5, ['1069', '5265', '349', '1111', '8939', '2645', '1783', '3819', 'U', '5327', '8503', '7829', 'M', 'V', 'H', '6043', 'C', '2561', 'T', '7305', '147', '6099', '4261', '4877']
Example Output:
10050