- #1
srfriggen
- 306
- 5
Homework Statement
Using the geometric series formula, a/1-r , where l r l < 1, it is easy to see that:
1/10 + 1/10(1/10)^2 + 1/10(1/10)^3... = 1.
applying the same formula to say, 2/3 = .666... does not give the answer 7, but rather 20/27.
My question is, what is the intuition behind .999... = 1?
It is easy to prove, and seemingly obvious (my girlfriend said, "well sure, even if it is infinite you would always have a 9 at the end so all them would round up like a domino effect from the end". I said, "sure, but then why doesn't that work for .666?" and I'm stumped (obviously her intuition about rounding up isn't what matters. Can someone tell me what does?