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

For the general idea, imagine you have a plank one meter long, and you take half of it, add 1/4 which is half of the half left, then again half of what was left again, and so on, you can “sense” that it all adds up to the complete plank if you go on long enough (you’re adding slices of atoms).

For the math, think about it the other way. How do you prove 0.99999999… is different from 1? Their difference would not be zero, let’s say “x”. Whatever x might be, you can show the real difference is even smaller, again and again. The only value that works is if x=0, so they are the same.

Note: it’s hard to stick to the “like I’m 5” rule!