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.

1, 2, ['5605', '6415']
12020

1, 2, ['2333', '6101']
8434

2, 4, ['P', 'C', '8927', 'H']

8927