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: 1, 4, ['261', '6237', '3809', '1857']
Example Output: 12164

Example Input: 2, 3, ['3335', '3451', 'f', 'M']
Example Output: 3451

Example Input: 6, 22, ['O', '5647', '2053', 'N', '8335', 'G', '2875', '8843', '4917', '4619', '6503', 'R', 'U', 'w', '299', '1525', '9943', '1477', 'w', 'u', '7561', '575', 'Q']
Example Output:
49137