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: 6, 12, ['q', '8055', '5233', '5529', 'T', 'h', 'w', 'w', '9449', 'W', '7903', 'b', '6925']
Example Output: 17352

Example Input: 1, 10, ['N', 'p', 'z', '6083', 'x', 'x', '3063', 'Y', '7099', '9961', 'k', '7365', 'e', '8629', '9595', '2831', '3649', '3809', 'm']
Example Output: 26206

Example Input: 2, 3, ['g', '9509', 'f', 'w']
Example Output:
9509