1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

What are the sub sequances here

  1. Dec 12, 2008 #1
    1/2 , 1/3 , 2/3 , 1/4 , 2/4 , 3/4 , 1/5 ,2/5 ,3/5 ,4/5 ...

    i cant see the patterns here?
     
  2. jcsd
  3. Dec 12, 2008 #2
    There are infinitely many subsequences of any sequence: just delete some elements.

    For the pattern, first look at the denominators only, and then look at how the numerators change for each denominator.
     
  4. Dec 12, 2008 #3
    ok i see numbers
    1/2 2/3 3/4
    a1 a3 a6
    but they dont have constant gap between then

    so i cant do a formula for that
     
    Last edited: Dec 12, 2008
  5. Dec 12, 2008 #4
    I see two things going on here... the denominator increases, and with each new denominator d a sum of 1/d to (d-1)/d fractions. If you are familiar with programming this sequence would easily be described with a nested loop.

    That should get you started ;)
     
  6. Dec 12, 2008 #5
    i see that too but i need to break into sUb sequences

    what you say doesnt help me with that
     
  7. Dec 12, 2008 #6
    As previously stated there are infinite subsequences in this sequence... is the original question more specific?
     
  8. Dec 12, 2008 #7
    ok i need at least two
    and their location n(k) formula
     
  9. Dec 12, 2008 #8
    To describe the sequence 1, 3, 6, 10, 15, ...,

    n(1) = 1
    n(2) = n(1) + 2
    n(3) = n(2) + 3
    ...
    n(k) = ?

    If you are familiar with Pascal's triangle, you can get a "nicer" expression from it.
     
  10. Dec 12, 2008 #9
    this is a recursion
    i need linear n(k) formula
     
  11. Dec 12, 2008 #10
    edit:

    Take the numbers with numerator 1. They clearly form the sub-sequence 1/(k+1) k=1...∞

    Now, these occur at:
    1/2 -> position 1
    1/3 -> position 2
    1/4 -> position 4
    1/5 -> position 7
    1/6 -> position 11
    1/n -> position ??

    Hint: the distance between positions increases by one every time
    Double hint: ½n² + ½n + 1
     
    Last edited: Dec 12, 2008
  12. Dec 12, 2008 #11

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    One thing I see is 1/2, 2/3, 3/4, 4/5, ... which clearly converges
    Another is 1/3, 1/4, 1/5, ... which also converges.

    As has been pointed out there are an infinite number of subsequences in any sequence. Perhaps a better question would be, "What are the subsequential limits?"
     
  13. Dec 13, 2008 #12
    i need to find the sub sequences in order to find their limits
    so there may be endless number of limits

    unless this series converges
    in which case all of the sub sequences limits equal
    the limit of the sequence

    what to do in this case:
    1/2 , 1/3 , 2/3 , 1/4 , 2/4 , 3/4 , 1/5 ,2/5 ,3/5 ,4/5 ...

    ??
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: What are the sub sequances here
  1. Whats wrong here? (Replies: 2)

  2. Trig Sub or what? (Replies: 3)

  3. What is the mistake here (Replies: 12)

Loading...