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, 2, ['9797', '5585', '1849', '4485', '9225']
Example Output: 5585

Example Input: 8, 17, ['9339', 'p', 'X', '1257', 'H', 'e', 'u', '7593', '4395', 'x', '5865', 'H', '3875', '1305', 'a', '3901', 'G', 'm', '6667', 'T', 'v', 'S', 'O', 'X', 'o', '8161', 'n', 'b', '3393', 'f']
Example Output:
26934