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Interesting problem

  1. Mar 27, 2007 #1
    we have to prove that

    10+100+1000+10000+100000+.........=-(1/9)

    any ideas?
     
  2. jcsd
  3. Mar 27, 2007 #2
    maybe you are trying to "prove" that
    10+100+1000+10000+100000+.........=-(10/9)

    here is a "proof" :)

    let
    S = 10 + 100 + 1000 + 10000 + ...

    then
    10S = 100 + 1000 + 10000 + ...

    now,
    S - 10S = 10
    => -9S = 10
    => S = -(10/9)
    => 10 + 100 + 1000 + 10000 + ... = -(10/9)
     
  4. Mar 27, 2007 #3
    i dunno maybe this is what i actually was looking for.
     
  5. Mar 27, 2007 #4
    but note that what i have given as a "proof" is not really a proof at all. the series 10 + 100 + 1000 + ... doesn't converge. so my "proof" doesn't actually work.
     
  6. Mar 27, 2007 #5
    so Murshid_islam what is the deal here? I can see that the series does not converge, however where is the problem on your proof? Is there a mathematical error, cause i could not see it, or what can we say about this?
     
  7. Mar 27, 2007 #6
    The error was when he subtracted the two and got a fixed real number. Subtracting infinity from infinity is not a well-defined operation.
     
  8. Mar 27, 2007 #7

    arildno

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    Because, in his expression for 10S, he ignored the largest term present there.
     
  9. Mar 27, 2007 #8
    as long as we are talking for infinit large numbers i cannot grasp how could there be a larger number on 10S than on S.I think it is absurd to talk about a "largest"term here, as long as we deal with infinit large terms! however i do understand the error now. SO defenitely we can say that
    10+100+1000+10000+100000+.........=-(10/9)

    is not mathematically true, and i cannot count on it, right?
     
    Last edited: Mar 27, 2007
  10. Mar 27, 2007 #9

    HallsofIvy

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    I would have thought it obvious from the start that a sum of positive numbers cannot be negative!

    Yes, I recommend that you not count on it!
     
  11. Mar 27, 2007 #10
    why don't you use sum of infinite G.P?
     
  12. Mar 27, 2007 #11
    What does G.P mean at first place? I am sorry i am not used to these, so i really don't know what they stand for?
    can you tell me?
     
  13. Mar 27, 2007 #12
    Yeah, i also thought it could not be negative. However i saw this on a tv scientific show, and a proffesor demonstrated this, so i just wondered how that would be possible. That proffesor, whose name i cannot remember, said that he had turned this for a mathematical test to prove that this is right. If ,at first place, this is exactly what i saw, couse i am not 100% posotive.
     
  14. Mar 27, 2007 #13
    G.P - Geometric Progression

    It is a series in which each term, apart from the first, is a fixed multiple of the previous term.

    a + ar + ar^2 + ar^3 + ...+ar^n+...

    The sum of the first n terms of such a series is a(1-rn)/(1-r). Check what happens for your series, when n tends to infinity.
     
  15. Mar 27, 2007 #14
    thnx, i do know what a geometric progression is, but just did not know that g.p stands for that.
    thnx indeed.
     
  16. Mar 27, 2007 #15
    i think after we find the sum of that geometric progression using a(1-rn)/(1-r), and if we evaluate the limit of the result, it turns out that the sum must be infinity. Is that right?
     
  17. Mar 27, 2007 #16
    Yes, it diverges.

    But, as mentioned earlier, the thing that should first convince you that the statement is not true is that the a sum of positive numbers cannot give you a negative number.
     
  18. Mar 27, 2007 #17
    yeah, thank you guys for your help.
     
  19. Mar 27, 2007 #18
    the error was when i let S = 10 + 100 + 1000 + .....
    As the series doesn't converge i cannot let it equal to a number S.
     
  20. Mar 27, 2007 #19
    Funny coincidence, but this Friday a prof at m university is giving a talk on why 1+2+4+6+...=-1 in the 2-adic numbers.
     
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