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.

[Q]: 1, 4, ['261', '6237', '3809', '1857']
[A]: 12164


[Q]: 2, 8, ['4517', 'w', '9145', '5477', '7679', 'j', '8603', 'z']
[A]: 30904


[Q]: 1, 6, ['T', '3841', 'D', '3909', 'f', '4099', '325']
[A]:
11849