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.
3, 13, ['2969', '8223', '1483', 'b', '1819', 'm', 'H', '7669', '5699', 'v', 'T', 'c', 'j', 's', '5257', 'Y', '4665', '4307', '4993', '3587', '4893', '2317']