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.
13, 19, ['9713', '8553', '3663', 'F', 'Z', 'D', 'P', 'g', '3483', '2691', 'S', '7973', '6721', '7193', '5975', 's', 'j', '2389', 'f', '6047', '9661', 'r', '1747']