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: 5, 9, ['125', 'A', 'E', 'X', 'j', '319', 'm', '7037', 'g', 'D', 'g', '6737', 'z', '5249']
Example Output: 7356

Example Input: 2, 15, ['r', '3527', 'Z', '9011', 'm', '879', '5305', '7153', 'c', '3567', 'd', '2319', 'M', 'y', '7703', '4899', 'G']
Example Output: 39464

Example Input: 8, 11, ['l', '3885', 'E', '8763', '4735', '8599', '3227', '3955', '2145', 'R', '5833', '6741', '855', '2391', 'H', 'j', 'C', 'b', 'w']
Example Output:
11933