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: 2, 10, ['143', '3769', '197', '3281', '1839', '8009', 'J', '1019', 'Z', 'y', 'M', 'w', '827', '3603', 'r', '6401', '1039']
Example Output: 18114

Example Input: 2, 12, ['8519', 'c', '7575', '1517', '2735', '4339', '7765', '6455', 'D', 'G', '2437', '9663', '3765', '299', 'n', '7921', 't', 'M', 'l', '515']
Example Output: 42486

Example Input: 11, 13, ['m', 'S', '6827', '7813', 'G', 'V', '903', 'Q', '2645', 'y', 'M', 't', '583', 'D']
Example Output:
583