Notices
Results 1 to 7 of 7

Thread: Begining from 1+1+1...+n

  1. #1 Begining from 1+1+1...+n 
    Suspended
    Join Date
    Jun 2012
    Posts
    344
    I have been interested in this paticular problem:



    Either there may be a general formula, or there's a systematic method.

    I decided to begin by looking at smaller values of m, and hopefully I can find a pattern in the formula.







    And so on...

    I've found two systematic ways to calculate formulas for higher values of m. The first uses simple algebra, the second involves derivatives.

    I'll be happy to share them later, but first I want to see if anyone got their own method that they would like to share. Please post below.


    Reply With Quote  
     

  2.  
     

  3. #2  
    Forum Freshman
    Join Date
    Jun 2006
    Posts
    93
    Quote Originally Posted by Wise Man View Post
    I have been interested in this paticular problem:



    Either there may be a general formula, or there's a systematic method.

    I decided to begin by looking at smaller values of m, and hopefully I can find a pattern in the formula.







    And so on...

    I've found two systematic ways to calculate formulas for higher values of m. The first uses simple algebra, the second involves derivatives.

    I'll be happy to share them later, but first I want to see if anyone got their own method that they would like to share. Please post below.
    If you don't need an exact equation then

    for x= 1 to n, ∑ xm ≈ ∫ xm = nm+1/(m+1).

    The approximation gets better with large n, as your three examples will show.


    Reply With Quote  
     

  4. #3  
    Forum Ph.D.
    Join Date
    Jul 2008
    Location
    New York State
    Posts
    996
    http://atsol.fis.ucv.cl/dariop/sites...ij_Engl._2.pdf

    Above has explicit formulas up to 7th power.
    Reply With Quote  
     

  5. #4  
    Forum Freshman
    Join Date
    Jun 2006
    Posts
    93
    Quote Originally Posted by mathman View Post
    http://atsol.fis.ucv.cl/dariop/sites...ij_Engl._2.pdf

    Above has explicit formulas up to 7th power.
    A great source!
    Reply With Quote  
     

  6. #5  
    Forum Ph.D. merumario's Avatar
    Join Date
    Nov 2012
    Location
    nigeria
    Posts
    844
    IMO,you can actually see it as a sequence an A.P as it appears to increase with a particular vale of 1^m.

    when i did that you will have n(2^m+1^m(n)-1^m)/2 (sum of an A.P).
    "I am sorry for making this letter longer than usual.I actually lacked the time to make it shorter."###
    Reply With Quote  
     

  7. #6  
    Forum Ph.D. Dave Wilson's Avatar
    Join Date
    Nov 2009
    Location
    Northumbria UK
    Posts
    979
    Quote Originally Posted by mathman View Post
    http://atsol.fis.ucv.cl/dariop/sites...ij_Engl._2.pdf

    Above has explicit formulas up to 7th power.
    I am very disappointed to see, that your link has eff all to do with maths.
    Latinos are Republican. They just don't know it yet.
    Ronald Reagan
    Reply With Quote  
     

  8. #7  
    Forum Ph.D.
    Join Date
    Jul 2008
    Location
    New York State
    Posts
    996
    Quote Originally Posted by Dave Wilson View Post
    Quote Originally Posted by mathman View Post
    http://atsol.fis.ucv.cl/dariop/sites...ij_Engl._2.pdf

    Above has explicit formulas up to 7th power.
    I am very disappointed to see, that your link has eff all to do with maths.

    ?????????????????????????????????????????????????? ????????????????????????
    Reply With Quote  
     

Similar Threads

  1. The begining of Earth
    By Mateja78 in forum Scientific Study of Religion
    Replies: 10
    Last Post: August 11th, 2012, 12:01 PM
  2. Begining of the end?
    By in forum Biology
    Replies: 5
    Last Post: January 25th, 2008, 03:34 PM
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
  •