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!

Series question

  1. Dec 23, 2005 #1
    Hi, I'm trying to figure out the average age in a solera process. The equations are:

    An = (2/3)(An-1 + 1) + (1/3)(0)
    Bn = (2/3)(Bn-1 + 1) + (1/3)(An-1 + 1)
    Cn = (2/3)(Cn-1 + 1) + (1/3)(Bn-1 + 1)

    With initial state:

    A0 = 0
    B0 = 0
    C0 = 0

    The question is, what is C as n goes to infinity?
     
  2. jcsd
  3. Dec 27, 2005 #2

    Fermat

    User Avatar
    Homework Helper

    Find the limiting value of An as n -> infinity.
    Substitute this value into the difference eqn for Bn.

    Find the limiting value of Bn as n -> infinity.
    Substitute this value into the difference eqn for Cn.

    And finally, find the limiting value of Cn as n -> infinity.

    I also wrote a small program to work out the values of the series, and got the limiting value for Cn as Cn = 8.00000....
     
    Last edited: Dec 27, 2005
  4. Dec 28, 2005 #3

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    If you assume that they all converge to a, b and c respectively then they satisfy

    a=(2/3)(a+1) + 1/3

    b=(2/3)(b+1) +(1/3)(a+1)

    c = (2/3)(c + 1) + (1/3)(b + 1)

    which you can solve.

    So, if there is a solution, that is what it is. You might need to prove that a limit exists, though.
     
  5. Dec 28, 2005 #4
    Hey, thanks for the help guys.

    Ya, I figured out later to just substitute a_n = a_n+1 and solve. I suppose I should prove that the series converges, but this is good enough for now.

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

Have something to add?



Similar Discussions: Series question
  1. Series question (Replies: 2)

  2. Series Question (Replies: 8)

  3. Series Question (Replies: 1)

  4. Series Question (Replies: 2)

  5. A series question (Replies: 4)

Loading...