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, 4, ['L', '8053', '8121', 'J', 'H', '7591', 'U', 'm']
Example Output: 16174

Example Input: 2, 10, ['f', 'r', 'Z', '1989', '5035', '1623', '9335', '7495', '8663', '2199', '2047', 'o']
Example Output: 36339

Example Input: 1, 2, ['1865', '9535', 'W', '7997', 'y', '1665', '9169', '7505']
Example Output:
11400