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, 3, ['F', 'N', 'N', 'r', 'X', 'R', '3477', 'T', 'z', 'v', 'B', 'Q']
Example Output: 0

Example Input: 2, 10, ['N', 'K', '4585', 'd', '8219', '3831', 'e', '7037', 'h', 'd', 'c', '577', 'c', '3559', '4059', 'M', '5349', 'V', 'L', '1807']
Example Output: 23672

Example Input: 17, 18, ['5889', '3243', 'k', 'K', '1167', 'Q', '5159', 'T', 'N', 'w', '3379', 'L', '1507', 'H', '7513', '2525', '7821', '3313', '6303', '5823', 'm', 'l', 'j', 'O']
Example Output:
11134