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!

Increasing or Decreasing Sequence

  1. May 1, 2012 #1
    A sequence (an) is defined recursively by a1 =1 and an+1 = 1/ 2+an for all n is greater than 1 or equal 1.

    ı'll prove that this sequence is convergent,buy ı cannot decide whethet it is increasing or decreasing .When ı write terms ,some terms increase some terms decrease.
     
  2. jcsd
  3. May 1, 2012 #2

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    What are the first couple of terms that you got? From the definition in your post it seems like the sequence is increasing to me
     
  4. May 1, 2012 #3
    a1=1/3,a2=7/21,a3=3/7,a4=7/17,a5=17/41 ......

    according to my calculation, a1>a2, a3>a2, a5>a4, a3>a4

    How can ı decide?
     
  5. May 1, 2012 #4

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    I suspect that your OP is not very well formatted now. Is the sequence
    an+1 = (1/2)+an (which is what you wrote using proper order of operations)

    or is it

    an+1=1/(2+an)
    which seems to match your most recent post

    If it's the latter, then just like you described in your post it's neither increasing nor decreasing
     
  6. May 1, 2012 #5
    My sequence is the second one.If it is neither increasing or decreasing ,how will ı show that it is convergent sequence? ı think there is a problem about sequence.

    Thank you for efforts :)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Increasing or Decreasing Sequence
  1. Increasing Sequence (Replies: 1)

Loading...