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.
7, 13, ['4725', '3471', '289', '2769', '1723', 'J', '7205', '2667', 'S', 'J', '4551', 'v', 'V', '9561', 'a', 'P', '5137', '7897']