Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
PhoenixFire
Group Title
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 \[1=1\]
 one year ago
 one year ago
PhoenixFire Group Title
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 \[1=1\]
 one year ago
 one year ago

This Question is Closed

PhoenixFire Group TitleBest ResponseYou've already chosen the best response.0
However, 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.
 one year ago

PhoenixFire Group TitleBest ResponseYou've already chosen the best response.0
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.
 one year ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.1
\[\infty\infty\neq0\]
 one year ago

PhoenixFire Group TitleBest ResponseYou've already chosen the best response.0
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?
 one year ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.1
http://www.vitutor.com/calculus/limits/indeterminate_forms.html
 one year ago

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

PhoenixFire Group TitleBest ResponseYou've already chosen the best response.0
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
 one year ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.