How does the sum of 1/2 + 1/4 + 1/8 etc. (Halves each time) eventually become 1? I understand it’s infinite but surely it still wouldn’t work?

Question

How does the sum of 1/2 + 1/4 + 1/8 etc. (Halves each time) eventually become 1? I understand it’s infinite but surely it still wouldn’t work?

In: Mathematics

Answer 1

Congrats, you just stumbled across Zeno’s Paradox.(Kinda)

The short answer is because infinity. When you are adding half of something infinitely you approach an infinitely small portion so it ceases to be useful to measure.