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.
1, 13, ['9255', '1193', 'v', '5609', 'H', '6419', '2917', '5481', '2319', '1677', 'X', '8397', '3327', '1673', 'A', 'O', 'w', 'Y', '305', '2127', '4003']