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: 1, 6, ['H', '7937', '9919', 'G', 's', '1929', '8585', 'n', 'u', 'J', 'C', '387']
Example Output: 19785

Example Input: 11, 20, ['8031', 'v', 'p', '4015', 'v', '3299', '4143', '445', 'I', 'L', 'm', 'u', '7963', '8085', 'c', 'k', 'I', 'A', '8433', '1897', 'g', 'x', '5935', '5195', 'W', 'j', 'A']
Example Output: 26378

Example Input: 2, 2, ['H', 'i']
Example Output:
0