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: 4, 10, ['C', '6511', 'S', '5389', '5679', 'O', 'Z', 'm', 'p', '1135', '7887', '6407', '6561']
Example Output: 12203

Example Input: 6, 6, ['I', '8721', '6901', '737', '5767', '9771', 'h']
Example Output: 9771

Example Input: 15, 19, ['7347', 'k', '4659', '2443', 'V', '8141', 'g', 'Y', '8009', 'i', '4779', '9361', 'M', 'w', '4833', '2443', '4233', '2161', 'H', 'F', '4521']
Example Output:
13670