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  1. Z

    Limit of factorial functions

    Thanks for the replies! The method hapefish proposed worked very vell. The sum diverges by the comparison test with the harmonic series. I also solved the problem using stirlings formula, thanks a lot guys! :)
  2. Z

    Limit of factorial functions

    Homework Statement Show that the folowing holds: \lim_{n\to\infty} \frac{(n!)^2 4^n}{(2n)!} = \infty Homework Equations It can be shown that \frac{(n!)^2 4^n}{(2n)!} = \prod_{k=1}^n \frac{4k}{k+n} The Attempt at a Solution If I can proove that \lim_{n\to\infty} \ln\left[\frac{(n!)^2...
  3. Z

    Reformulating exact values

    Yes. My english sucks, I know :P
  4. Z

    Reformulating exact values

    Yes, I know. I'm a bit sceptical my self. But he is a really smart guy and has also study math like me. The problem is that he is no so old that he can't remember anything :P But if there is no solution without trig or i-s, then we shuld be able to prove it?
  5. Z

    Reformulating exact values

    Well, the original problem is to solve for x here: http://folk.ntnu.no/jonvegar/images/flaggstangoppgaven.jpg [Broken] Which lead to: [PLAIN][PLAIN]http://folk.ntnu.no/jonvegar/images/math.gif [Broken] This will lead to a 3.degree-equation. And the result is a answer with either...
  6. Z

    Reformulating exact values

    Well, it's just for fun actually. My grandfather is claim that he has solved it, but he can't recall how. So I only got he's word for it. But I really want to solve the problem. He claimed that he solved it when he was at my age (21), so I got a pressure to so too ;)
  7. Z

    Reformulating exact values

    Because I have tried for several years now :) But if you think it can be solved, be my guest ;)
  8. Z

    Reformulating exact values

    I don't think it is possible to solve this problem, all tho my grandfather say he has done it. (he can't remember how, but I guess he cheated...)
  9. Z

    Reformulating exact values

    But that doesn't give me an answer without trigonometrical components and imaginary numbers... And btw: [PLAIN]http://folk.ntnu.no/jonvegar/images/imaginary9.jpg [Broken] Thank you for LaTeX tip :smile:
  10. Z

    Solve cos((1/3)*arccos(x))

    Why are we not interested in the negative root?
  11. Z

    Reformulating exact values

    Homework Statement Find exact values for z without any trigonometrical components or imaginary numbers x = \frac{79}{60} + \frac{1}{30} \sqrt{6121} cos\left(\frac{1}{3}arccos(z)\right) where z = \frac{473419}{6121\sqrt{6121}} Homework Equations cos\left(\frac{1}{3}arccos(z)\right) =...
  12. Z

    Solve cos((1/3)*arccos(x))

    The problem of this thread is actually solved. Maybe I shall make a new thread about my main goal...
  13. Z

    Solve cos((1/3)*arccos(x))

    Yes, and this is what I get. I guess that's the far as I am going to get: cos(\frac{1}{3}arccos(x)) = \frac{(x + \sqrt{x^2-1})^{1/3}}{2} + \frac 1 {2(x+\sqrt{x^2-1})^{1/3}} But again, my x is defined as x = \frac{473419}{6121\sqrt{6121}} approximate x = 0.9885806704. So my final goal here...
  14. Z

    Solve cos((1/3)*arccos(x))

    2y=eix+e-ix z=eix 2y=z+z-1 2yz=z2+1 z2-2yz+1=0 z=(y+(y2-1)0,5) or z=(y-(y2-1)0,5) eix=(y+(y2-1)0,5) or eix=(y-(y2-1)0,5) ix=ln(y+(y2-1)0,5) or ix=ln(y-(y2-1)0,5) x=i-1ln(y+(y2-1)0,5) or x=i-1ln(y-(y2-1)0,5)
  15. Z

    Solve cos((1/3)*arccos(x))

    Well, I can make a new thread where you have to get rid of the i-s... This is not any schoolwork so I have all the time in the world :smile: I have tried what's in post #26 with no result How do you get an expression for x, when you got both eix and e-ix? And even if I get an expression for...
  16. Z

    Solve cos((1/3)*arccos(x))

    No. The problem is not solved because i still have not got rid of the i-s. And that is not a trivial thing to do in my expression...
  17. Z

    Solve cos((1/3)*arccos(x))

    How do you get an expression for x, when you got both eix and e-ix? And even if I get an expression for arccos without i-s, I still have to get rid of cos...
  18. Z

    Solve cos((1/3)*arccos(x))

    I want an answer to this problem:
  19. Z

    Solve cos((1/3)*arccos(x))

    Is it really no one that can give me an answer to this problem??
  20. Z

    Solve cos((1/3)*arccos(x))

    Ok, here is what I have done: http://folk.ntnu.no/jonvegar/images/imaginary3.png [Broken] http://folk.ntnu.no/jonvegar/images/imaginary2.png [Broken] [PLAIN][PLAIN]http://folk.ntnu.no/jonvegar/images/imaginary4.png [Broken] But when I'm testing my result in maple I get "false"...
  21. Z

    Solve cos((1/3)*arccos(x))

    Can you define Count Iblis' method for me?
  22. Z

    Solve cos((1/3)*arccos(x))

    Belive me, I have tried. But I don't understand the answer i get if I use the 2. method: [PLAIN]http://folk.ntnu.no/jonvegar/images/imaginary.jpg [Broken] I want a answer without any imaginary parts. My x is defined only for [0,9], but when I cancel the imaginary part I do not get the...
  23. Z

    Solve cos((1/3)*arccos(x))

    Hmmm, it shall be possible to write the equation without any logarithms. If it is so easy, can you just write down the formula for me? :smile: I need it actually just to solv an other problem.
  24. Z

    Solve cos((1/3)*arccos(x))

    Maple says: [PLAIN]http://folk.ntnu.no/jonvegar/images/capture.png [Broken] It did not work. I still need help! :smile:
  25. Z

    Correlation between science and atheism/agnosticism

    As Riachard Dawkins self put it: "Evolution is a fact" http://richarddawkins.net/thegreatestshowonearth" [Broken] The flying spaghettimonster is a argument atheist shall use. http://www.youtube.com/watch?v=vk8EANdpAj0&playnext_from=TL&videos=9xrUGG_-QLU" Invent your own monster :P
  26. Z

    Correlation between science and atheism/agnosticism

    Oh, I'm sorry then. It's just my way to talk. I'm from Norway, so I suppose that our expressions can't be directly translated. And my english sucks. :smile: I'm never rude :smile:
  27. Z

    Correlation between science and atheism/agnosticism

    What is "the supernatural" for you then? Do you have any definition?
  28. Z

    Correlation between science and atheism/agnosticism

    I know. It's is not any documentation. So just relax. It is just to be interesting :smile: I have founded what I wanted so far in the poll :smile:
  29. Z

    Correlation between science and atheism/agnosticism

    Right. I'm actually most interested in the poll
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