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.

4, 6, ['4301', 'a', 'E', '3709', '5105', 'B']
8814

1, 2, ['2333', '6101']
8434

5, 6, ['6965', 'b', '3333', 'l', 'j', '1299', '1389']

1299