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, ['3949', '5315', 'G', 's', 'v', 'm', '7833', 'E', 'j']
Example Output: 0

Example Input: 4, 4, ['t', 'Z', '8689', 'I', '5589', 'H', 'Z']
Example Output: 0

Example Input: 3, 6, ['B', '9793', '3257', '1205', 'h', '3933', '7375', '7421', 'N', '4269', '6193']
Example Output:
8395