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: 9, 11, ['6655', 'V', 'm', '3229', '2427', '9165', 'F', 'c', 'K', '3925', '1261', '1055', 'S']
Example Output: 5186

Example Input: 9, 12, ['4189', '4575', 'i', 'e', 'Y', '5595', 'U', 'M', 'b', 'n', '5347', 'v', 'w', 'Z', 'F', '503', 'G', '4429', '3087', '295', 'W']
Example Output: 5347

Example Input: 4, 14, ['2943', 'X', 't', '2549', '8015', '7731', 'z', '4401', 'f', 'S', '3841', '4475', '6379', 'a', '1199', 's', '7845', '6091', '1641', '6355']
Example Output:
37391