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: 4, 10, ['C', '6511', 'S', '5389', '5679', 'O', 'Z', 'm', 'p', '1135', '7887', '6407', '6561']
Example Output: 12203

Example Input: 5, 10, ['3907', '1629', 'v', '6711', '8347', 'E', '4067', 'T', '1665', '5735', '4879']
Example Output: 19814

Example Input: 3, 5, ['4047', 'F', 'e', '7173', 'q', 'g', '6203', 'A']
Example Output:
7173