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: 14, 20, ['4221', '2381', 'i', 'm', 'c', 'F', '9703', '3529', 'a', '83', 'D', '1023', 'I', 'c', 'W', '7163', '341', 'w', '7855', '2317', '8989', '3629', 'b']
Example Output: 17676

Example Input: 1, 14, ['T', 'y', 'L', 'l', '5307', 'j', '2235', '9617', 'e', '7687', 't', '4357', '1745', 'X', '8485', 'a', '1387', '1351', '6437', 'u']
Example Output: 30948

Example Input: 17, 17, ['x', '4093', 'z', '8933', '7091', '2615', '7693', 'P', '1815', '1745', 'k', 'H', 'u', '9567', '5089', 'R', '6783', '5471', 'C', 'B', 'n', 'J', '2139']
Example Output:
6783