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.
12, 13, ['8731', 'P', 'S', '2905', '929', '2239', 'a', '353', 'z', '6987', 's', 'S', '4459', 'y']