## PhoenixFire 3 years ago I saw this a little while ago and wanted to figure out how to prove that it's invalid. $1+2+4+8+...+\infty= -1$ Proof is as follows: Knowing that $1 * x=x$ and that $2-1=1$ we can say that $(2-1)(1+2+4+8+...+\infty)= -1$expanding the brackets you get$2+4+8+16+...+\infty- 1 - 2-4-8-...-\infty= -1$ everything from 2 up cancels leaving $-1=-1$

1. PhoenixFire

However, if you do it for anything up to but NOT including infinity it is wrong. $(2-1)(1+2+4)=2+4+8-1-2-4=8-1=7$Clearly not -1.

2. PhoenixFire

Something to do with Divergent Series. but I don't understand it. $\sum_{n=0}^{\infty}2^n$ So I'm basically looking for a way to disprove the above claim for infinity.

3. UnkleRhaukus

$\infty-\infty\neq0$

4. PhoenixFire

What do you get in the case of $\infty - \infty=?$Is there some law or rule that you can refer me to that explains that it's not equal to zero?

5. UnkleRhaukus
6. UnkleRhaukus

infinity is not a number so you cant always treat it like a number, some times you indeterminate forms

7. PhoenixFire

Well that makes sense now. I've always treated infinity as something unique and not a number, but when it came to this my brain got fried. Thanks, @UnkleRhaukus