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, 13, ['9225', '8983', 'E', 'F', 'L', 'V', 'h', '9233', '8887', 'o', 'd', 'U', 'B', 'u']
Example Output: 36328

Example Input: 2, 9, ['4437', 'g', 'I', 'u', '4299', '45', '4397', '5327', '5301', 'J', 'K', '4129', 'W', '8567']
Example Output: 19369

Example Input: 11, 19, ['6075', 'P', '6073', '4525', '8585', 'A', 'F', '4727', '5', '8935', 'c', 'i', '1657', '4127', '343', 'm', '3593', 'M', '6203', '3515', '3925', '741', '8547', 'l', '2013']
Example Output:
15923