Build a Convergent Tower

Take a long paper strip and fold the right half over onto the left. Now fold just the leftover half again, and again. The folded length grows toward the full strip but never passes it — each fold adds half of what remains. That is a convergent sequence: the leftover shrinks toward zero while the total approaches a finite limit, exactly how an infinite series settles on a finite sum.

Now try the visual version. Draw a line exactly 10 cm long. Mark the halfway point (5 cm). Then mark 7.5 cm, halfway across what is left. Then 8.75 cm. Keep going. Each mark lands closer to 10 cm but never quite reaches it — convergence you can see with a ruler.