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: 2, 2, ['5189', 'J']
Example Output: 0

Example Input: 19, 21, ['y', '9403', 'C', '389', '5521', '9271', 'W', 'B', '3613', 'w', '2741', 'H', '8305', '727', '7641', '5857', '9183', '1297', 'p', '7371', 'b']
Example Output: 7371

Example Input: 5, 6, ['F', '8727', 'm', '3655', '2957', '1593', 't', 'C']
Example Output:
4550