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: 21, 23, ['211', '959', '3183', '1605', '3217', '6793', '2239', 'Z', 'T', 'f', '2559', '9249', 'X', '6925', '4373', 'j', 'H', '9575', '3481', 'W', 'p', 'v', 't', '5995', '8765', '201', 'F', 'O', '7251', 'S']
Example Output: 0

Example Input: 1, 2, ['6121', '15', 'c', 'g']
Example Output:
6136