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: 3, 4, ['I', '8765', 'a', '719', '2555', 'w', '3437', '6159', 'e', '5239']
Example Output: 719

Example Input: 2, 9, ['7111', '835', 'W', '6975', '4459', 'B', 'B', 'Z', 'o']
Example Output: 12269

Example Input: 4, 5, ['3523', 'M', 'F', '5701', 'b', 'e']
Example Output:
5701