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: 1, 4, ['261', '6237', '3809', '1857']
Example Output: 12164

Example Input: 5, 8, ['5745', '5919', '2351', 'M', '3273', '6855', '2999', 's', 'F', 'o', 'W', '8607']
Example Output: 13127

Example Input: 1, 1, ['I', 'C']
Example Output:
0