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: 5, 10, ['7435', 'B', '7841', '5901', 'I', '6255', 'g', 'F', 'D', '1839', '3651', 'Q', '1629', 'T', '3423', 'y', '9597', '8453', '8541', 'a', '357', 'k', 'P']
Example Output: 8094

Example Input: 3, 4, ['F', '7341', 'P', '3315']
Example Output: 3315

Example Input: 9, 16, ['6245', '9149', 'C', '2477', '1883', '5443', '9463', 'F', 'U', 'F', '9611', '2731', '53', 'X', '8457', 'H', '1947', '357', '8869', '3705', '8069', '7705']
Example Output:
20852