The term "series" typically refers to the summation of a sequence of numbers. In mathematical terms, a series is the sum of the terms of a sequence, where the terms are indexed by the natural numbers. Therefore, the most accurate definition from your list is:
a summation of quantities whose positions are based upon the natural numbers.
This contrasts with a "sequence," which refers to the arrangement of quantities themselves. Thus, a series takes the elements from a sequence and sums them.