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.

Example Input: 13, 18, ['3475', 'o', '3353', '3225', 'I', '3297', 'Z', 'i', '7995', '5299', '7275', '3123', '1975', '4599', 's', '2489', '8733', 'N', '4563']
Example Output: 17796

Example Input: 3, 8, ['3403', 'r', '7273', 'g', 'O', 'A', '123', '2839', 'g', 'R', 'f', 'y', 'F']
Example Output: 10235

Example Input: 8, 15, ['N', '645', '2623', 'p', 'j', '7319', '9555', '2863', 'n', '2045', 'V', 'D', 'u', '3405', '6971', 'm', '8129', '5347', '1971', '829', '6709', 'H']
Example Output:
15284