Notices
Results 1 to 10 of 10

Thread: Iterated exponentiation

  1. #1 Iterated exponentiation 
    Forum Freshman
    Join Date
    Aug 2010
    Posts
    97
    Is there any way to find out what the following becomes?



    Thanks in advance!


    Reply With Quote  
     

  2.  
     

  3. #2 Re: Iterated exponentiation 
    Forum Isotope
    Join Date
    Feb 2009
    Location
    Transient
    Posts
    2,914
    Quote Originally Posted by m84uily
    Is there any way to find out what the following becomes?



    Thanks in advance!
    By this, do you mean, for n=6, or


    Wise men speak because they have something to say; Fools, because they have to say something.
    -Plato

    Reply With Quote  
     

  4. #3 Re: Iterated exponentiation 
    Forum Freshman
    Join Date
    Aug 2010
    Posts
    97
    Quote Originally Posted by Arcane_Mathematician
    By this, do you mean, for n=6, or
    Well the first one, I think. But just to clarify:



    Rather than:

    Reply With Quote  
     

  5. #4  
    Forum Radioactive Isotope MagiMaster's Avatar
    Join Date
    Jul 2006
    Posts
    3,440
    It should just approach 1. The nth root of anything less than 1 is closer to 1.
    Reply With Quote  
     

  6. #5  
    Forum Freshman
    Join Date
    Aug 2010
    Posts
    97
    Quote Originally Posted by MagiMaster
    It should just approach 1. The nth root of anything less than 1 is closer to 1.
    I don't think this is the case, it seems that the number lies somewhere between .65 and .7

    However if it was computed left to right and became then I would expect it to approach 1.
    Reply With Quote  
     

  7. #6  
    Forum Radioactive Isotope MagiMaster's Avatar
    Join Date
    Jul 2006
    Posts
    3,440
    Oh, right. I was reading it wrong. It might not converge. It looks like the evens and odds give two different answers. I don't think there's an easy way to calculate a closed form for either though. Power towers are typically complicated.
    Reply With Quote  
     

  8. #7  
    Forum Junior c186282's Avatar
    Join Date
    Dec 2008
    Posts
    208
    I agree with m84uily the result is and it does approach 1 very quickly

    Here are the first few values:

    0.79370052598409973738
    0.94387431268169349664
    0.98851402035289613536
    0.99807644357562873885
    0.99972497942011085466
    0.99996561829044151083
    0.99999617975167238799
    0.99999961797451049383
    0.99999996527040401417
    0.99999999710586695511
    0.9999999997773743809
    0.9999999999840981701
    0.9999999999989398780
    0.9999999999999337424
    0.9999999999999961025
    0.9999999999999997835
    0.9999999999999999886
    0.9999999999999999994
    Reply With Quote  
     

  9. #8  
    Forum Radioactive Isotope MagiMaster's Avatar
    Join Date
    Jul 2006
    Posts
    3,440
    You're reading it the way I did at first, but that's not actually what he's asking.

    The series would be:
    (1/2) = 0.5
    (1/2)^(1/3) = 0.7937
    (1/2)^((1/3)^(1/4)) = 0.5906
    ...

    The position of the parenthesis matters quite a bit when dealing with power towers.
    Reply With Quote  
     

  10. #9  
    Forum Junior c186282's Avatar
    Join Date
    Dec 2008
    Posts
    208
    Yes your right, MagiMaster it is more involved. However it does settle down kind of



    I do not know how to get at the limit analyticity but here are the computer values.

    2. 0.5
    3. 0.793701
    4. 0.590564
    5. 0.739735
    6. 0.622665
    7. 0.717776
    8. 0.637556
    9. 0.706797
    10. 0.645562
    11. 0.700619
    12. 0.650267
    13. 0.696884
    14. 0.653189
    15. 0.694526
    16. 0.655061
    17. 0.693002
    18. 0.656277
    19. 0.692011
    20. 0.657069
    21. 0.69137
    22. 0.657578
    23. 0.69096
    24. 0.6579
    25. 0.690704
    26. 0.658098
    27. 0.690549
    28. 0.658217
    29. 0.690458
    30. 0.658285
    31. 0.690406
    32. 0.658324
    33. 0.690377
    34. 0.658345
    35. 0.690362
    36. 0.658355
    37. 0.690354
    38. 0.658361
    39. 0.69035
    40. 0.658363
    41. 0.690349
    42. 0.658365
    43. 0.690348
    44. 0.658365
    45. 0.690347
    46. 0.658365
    47. 0.690347
    48. 0.658366
    49. 0.690347
    50. 0.658366
    51. 0.690347
    52. 0.658366
    53. 0.690347
    54. 0.658366
    55. 0.690347
    56. 0.658366
    57. 0.690347
    58. 0.658366
    59. 0.690347
    60. 0.658366
    61. 0.690347
    62. 0.658366
    63. 0.690347
    64. 0.658366
    65. 0.690347
    66. 0.658366
    67. 0.690347
    68. 0.658366
    69. 0.690347
    70. 0.658366
    71. 0.690347
    72. 0.658366
    73. 0.690347
    74. 0.658366
    75. 0.690347
    76. 0.658366
    77. 0.690347
    78. 0.658366
    79. 0.690347
    80. 0.658366
    Reply With Quote  
     

  11. #10  
    Suspended
    Join Date
    Oct 2011
    Posts
    42
    what this list is for ?
    Reply With Quote  
     

Bookmarks
Bookmarks
Posting Permissions
  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •