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: 2, 8, ['743', '3417', '5979', 'J', 'f', '4707', 'k', 'i', '2167', 'V', 'g']
Example Output: 14103

Example Input: 2, 20, ['7991', '1029', 'L', '3307', 'A', '6641', '8833', 'J', '2751', '7457', 'f', '943', 'D', '5609', '5123', '5561', 'N', '1755', '1117', 'C', 'k', '6657', '2569']
Example Output: 50126

Example Input: 5, 10, ['o', 'M', '2609', 'o', '1765', 'G', 'a', 'N', '4351', '8603', '7673', '1813', '8061']
Example Output:
14719