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, ['L', 'Z', '4501', '4131', 'a', '8057', 'K', 'P', '4713', '8889', 'b', '3927', 'k', '6005', 'T', 'w', 'S', '3963', '2727']
Example Output: 8889

Example Input: 1, 4, ['2025', '6689', '1227', '3943', 'z', '719', '8941', 'b', 'V', 'w', '5267', '2403', 'N', '5771']
Example Output: 13884

Example Input: 1, 1, ['5565', 'X', 'g', 'm', '291', '9563', 'u', '9359', 'N']
Example Output:
5565