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: 1, 1, ['R', '3969', 'O', '3281', 'X', '5173', 'K', 'G', 'm', 'Y', '4981', 'x', '9127', 'X', 'w', 'm', '3873', '5887', '7405', 't', 'P', 'K', '8459', '9699']
Example Output: 0

Example Input: 1, 2, ['2349', 's', '3165', 'O']
Example Output:
2349