Need a hard math problem

Discussion in 'Physics & Math' started by rian.wrenn, Sep 7, 2007.

  1. rian.wrenn Registered Member

    Messages:
    42
    I need a hard math problem so i can stump my teaher for extr credit. Pls, needs to be a good one and cant end with a theoracal answer. THX,

    Also anyone elts can solve it too
    thx
     
  2. Google AdSense Guest Advertisement



    to hide all adverts.
  3. paulfr Registered Senior Member

    Messages:
    227
    Sum of Coefficients

    What is the sum of the coefficients of
    ( [3x - 3x^2 +1]^744 ) x ( [- 3x + 3x^2 +1]^745 ) ??
     
  4. Google AdSense Guest Advertisement



    to hide all adverts.
  5. BenTheMan Dr. of Physics, Prof. of Love Valued Senior Member

    Messages:
    8,967
  6. Google AdSense Guest Advertisement



    to hide all adverts.
  7. Absane Rocket Surgeon Valued Senior Member

    Messages:
    8,989
    How about the one I am working on: Given a k-connected graph, two longest cycles meet at k or more vertices.
     
  8. Absane Rocket Surgeon Valued Senior Member

    Messages:
    8,989
    WTF? 1 + 1/2 + 1/3 + ... = -1/12?

    I MUST be missing something...

    By the way, n=1... because 1/n^s for n = 0 is a bad thing

    Please Register or Log in to view the hidden image!

     
  9. rian.wrenn Registered Member

    Messages:
    42
    just saying, DAMM you people are smart, like really really smart!!!!

    O and what calculater do you use when the equasionis come out as a picture
     
  10. BenTheMan Dr. of Physics, Prof. of Love Valued Senior Member

    Messages:
    8,967
    absane--it's just an analyitic continuation.
     
  11. Absane Rocket Surgeon Valued Senior Member

    Messages:
    8,989
    So -1/12 has a different meaning?

    Sorry, analysis is not my cup of tea.
     
  12. iceaura Valued Senior Member

    Messages:
    24,044
    Point. Ben might want to fix that.

    Does anyone know what that odd summation is good for? The link describes it as having properties useful for the study of divergent series - like what properties, exactly?
     
  13. Tom2 Registered Senior Member

    Messages:
    726
    Would you be so kind as to explain how summing infinitely many positive integers can possibly lead to a negative result.

    Please Register or Log in to view the hidden image!



    I did check them out. The wiki reference says that the series converges for all s such that Re(s)>1. -1 is not greater than 1. Unless of course you would like to explain how -1 can be analytically continued to be greater than 1.

    Please Register or Log in to view the hidden image!

     
  14. CANGAS Registered Senior Member

    Messages:
    1,612
    The query was focused on Tom2 asking how Tom2 can explain summing an unlimited number of positive integers.

    Tom2 has fouled off the query by invoking a third party ( and a notoriously unreliable one) rather than personally providing an opinion and a proof.

    There is no way in H(expletive deleted) that an unlimited quantity of positive integers can sum to a negative answer.

    In dreams many strange things are seen, so probably Tom2 is speaking of dream hallucinations rather than provable science matters.
     
  15. Pete It's not rocket surgery Moderator

    Messages:
    10,166
    CANGAS,
    Your animosity toward Tom2 seems to have blinded you. You might want to check who made the claim in question.
     
    Last edited: Sep 9, 2007
  16. CANGAS Registered Senior Member

    Messages:
    1,612
    I have expressed no animosity.

    Your expostulation which tries to form a thing which is not real is alarming.

    Do your doctors know of your tendencies to imagine animosities which are are not real?
     
  17. CANGAS Registered Senior Member

    Messages:
    1,612
    I repete:

    please explain in specific detail how any sum of positive integers can add up to be a negative answer.
     
  18. Pete It's not rocket surgery Moderator

    Messages:
    10,166
    :bugeye:
    It can't. Just as Tom2 said.
     
  19. CANGAS Registered Senior Member

    Messages:
    1,612
    So, as a kind of a parting shot, you cute little baby head thing, does the sum of an unlimited number of positive integers sum to a positive answer or a negative answer?

    Or do you have any clue ?
     
  20. Pete It's not rocket surgery Moderator

    Messages:
    10,166
    :runaway:
    Are you insane?
    Obviously it's positive infinity.
     
  21. Tom2 Registered Senior Member

    Messages:
    726
    Do you really have to ask?

    Please Register or Log in to view the hidden image!



    CANGAS, this is not some big mystery. Every one who's ever taken a full course in high school calculus knows that any p-series converges when p is greater than one, and diverges otherwise.
     
    Last edited: Sep 9, 2007
  22. D H Some other guy Valued Senior Member

    Messages:
    2,257
    Ben the Texan was toying with all of y'all, and it went over almost all of y'all's heads. To summarize, the Reimann zeta function is defined as

    \(\zeta(s) = \sum_{n=1}^{\infty} \frac 1 {n^s}\)

    By analytic continuation, \(\zeta(-1) = -1/12\) and thus, by analytic continuation,

    \(\zeta(-1) = \sum_{n=1}^{\infty} n = -1/12\)

    Nice trick, Ben. So what's wrong with this?

    Simple: The analytic continuation of some function f(z) is some function F(z) such that F(z)=f(z) everywhere f(z) is defined. Here, f(z) is the series definition of the zeta function and F(z) is its analytic continuation to the complex plane less the line \(\Re z = 1\). The original series diverges for \(\Re s <= 1\). The analytic continuation does not change the fact that the series diverges for s=-1.

    Edited to add:
    What Ben did was the analytic equivalent of the various devices using division by zero that "prove" 1=2.
     
    Last edited: Sep 9, 2007
  23. §outh§tar is feeling caustic Registered Senior Member

    Messages:
    4,832
    Riemann's hypothesis will do

    Please Register or Log in to view the hidden image!

     

Share This Page