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1+2+3+4+ =-1/12? proof

  1. Feb 20, 2014 #1
    I've see this neat proof:
    http://www.youtube.com/watch?v=E-d9...eature=iv&annotation_id=annotation_3085392237 (for some reason the youtube tag didn't work in preview...)
    And now I don't see how what I've learned about series convergence is true...
    I've been told that if [itex]a_n > b_n \forall n[/itex] then [itex] \sum a_n > \sum b_n [/itex] therefore, if [itex] \sum b_n [/itex] is divergent then, [itex] \sum a_n [/itex] must be too.
    Also, If the partial sum diverges, the series is said to be divergent, isn't it?
    And what about [itex] a_n \neq 0 [/itex] for n that tends to infinity?
    So many ways I could show this series diverges, yet he show it's equal to -1/12???

    Where am I, or is he, wrong?
     
    Last edited: Feb 20, 2014
  2. jcsd
  3. Feb 20, 2014 #2
    I think this cannot be true. The sum of all natural numbers up to N equals (as also shown in the end of the video) ## N(N+1)/2 ##. This obviously goes to infinity as N goes to infinity. And of course there is also no way how strictly positive numbers can add up to give a negative result.
     
  4. Feb 20, 2014 #3
    That's what I was saying :)
    So where is he wrong?
     
  5. Feb 20, 2014 #4
  6. Feb 20, 2014 #5

    Borek

    User Avatar

    Staff: Mentor

    And as this link was posted we can safely close the thread.
     
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