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PhoenixFire
 4 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 \[21=1\] we can say that \[(21)(1+2+4+8+...+\infty)= 1\]expanding the brackets you get\[2+4+8+16+...+\infty 1  248...\infty= 1\] everything from 2 up cancels leaving \[1=1\]
PhoenixFire
 4 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 \[21=1\] we can say that \[(21)(1+2+4+8+...+\infty)= 1\]expanding the brackets you get\[2+4+8+16+...+\infty 1  248...\infty= 1\] everything from 2 up cancels leaving \[1=1\]

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PhoenixFire
 4 years ago
Best ResponseYou've already chosen the best response.0However, if you do it for anything up to but NOT including infinity it is wrong. \[(21)(1+2+4)=2+4+8124=81=7\]Clearly not 1.

PhoenixFire
 4 years ago
Best ResponseYou've already chosen the best response.0Something 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.

UnkleRhaukus
 4 years ago
Best ResponseYou've already chosen the best response.1\[\infty\infty\neq0\]

PhoenixFire
 4 years ago
Best ResponseYou've already chosen the best response.0What 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?

UnkleRhaukus
 4 years ago
Best ResponseYou've already chosen the best response.1http://www.vitutor.com/calculus/limits/indeterminate_forms.html

UnkleRhaukus
 4 years ago
Best ResponseYou've already chosen the best response.1infinity is not a number so you cant always treat it like a number, some times you indeterminate forms

PhoenixFire
 4 years ago
Best ResponseYou've already chosen the best response.0Well 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
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