Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

PhoenixFire

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 \[-1=-1\]

  • one year ago
  • one year ago

  • This Question is Closed
  1. PhoenixFire
    Best Response
    You've already chosen the best response.
    Medals 0

    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.

    • one year ago
  2. PhoenixFire
    Best Response
    You've already chosen the best response.
    Medals 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
  3. UnkleRhaukus
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\infty-\infty\neq0\]

    • one year ago
  4. PhoenixFire
    Best Response
    You've already chosen the best response.
    Medals 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
  5. UnkleRhaukus
    Best Response
    You've already chosen the best response.
    Medals 1

    http://www.vitutor.com/calculus/limits/indeterminate_forms.html

    • one year ago
  6. UnkleRhaukus
    Best Response
    You've already chosen the best response.
    Medals 1

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

    • one year ago
  7. PhoenixFire
    Best Response
    You've already chosen the best response.
    Medals 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
    • Attachments:

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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.