Full Idea
The concept of a 'limit' allows for an infinite number of finite quantities to add up to a finite sum.
Gist of Idea
The modern idea of 'limit' allows infinite quantities to have a finite sum
Source
Adrian Bardon (Brief History of the Philosophy of Time [2013], 1 'Aristotle's')
Book Reference
Bardon,Adrian: 'Brief History of the Philosophy of Time' [OUP 2013], p.15
A Reaction
This is only if the terms 'converge' on some end point. Limits are convenient fictions.