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, 7, ['o', '3377', 'x', '9385', 'z', '9963', 'S', 'h', 'l', '1525', 'k']
Example Output: 22725

Example Input: 2, 4, ['3155', '581', 'N', '153', 't', '7941', '6065']
Example Output: 734

Example Input: 5, 13, ['H', 'o', '7719', '4705', '8191', 'r', '6315', 'X', '2791', 'p', 'I', 't', '3427']
Example Output:
20724