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: 7, 19, ['6719', 'c', 'S', '3259', '1287', 'u', '9251', '2183', '4821', '9449', 'I', 'P', 'i', '7597', '8141', 'G', 'j', '8587', '7245', 'G', 'O', 'o', '9479']
Example Output: 57274

Example Input: 5, 16, ['a', '2439', 'p', '6759', 'z', '2233', 'q', '1447', 'Y', 'k', 'Y', 'Y', '4489', 'N', '5251', '5367']
Example Output: 18787

Example Input: 9, 11, ['8245', 'w', '9851', '1393', 'Y', 'c', 'S', 'z', 'r', '1953', 'J', 'a', '975']
Example Output:
1953