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: 10, 11, ['J', '5319', '1625', 'z', '275', 'B', '6901', 'b', 'X', '8669', '2307', '3117', 'K']
Example Output: 10976

Example Input: 2, 5, ['5713', 'f', 'g', '9979', '2651', 't', '6513', 'v', '5733', '3325', 'M', 'B', '6139', 'n', 'K', 'h', 'c', '1181', '1263', '6625', 'F', '7059', 'c', '4083', 'i', 'g', '6783']
Example Output: 12630

Example Input: 1, 11, ['9771', 'w', '2225', '9261', '9353', 'N', '9315', '1237', '2081', 'I', '9731', '4337']
Example Output:
52974