Infinite series exist in mathematics and in the imagination, but they don't exist in actuality. An actual series must be finite. It cannot be infinite But, the argument went, if this "actual existence" is finite, something else must be anterior any series of motions. That's Aristotle, at least.
Or, in other words, there is a world of difference between an infinite series and infinite existence.
This distinction you make between infinity in mathematics or imagination is very important.