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: 3, 4, ['F', '7341', 'P', '3315']
Example Output: 3315

Example Input: 1, 1, ['5141', 'S']
Example Output: 5141

Example Input: 1, 8, ['5525', '3301', '7711', '943', '7487', 'Z', '907', '129', '8203', 'S', 'b', '6707', 'W', 'S', 'u']
Example Output:
26003