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How to determine convergence/divergence?

  1. Jan 14, 2012 #1
    1. The problem statement, all variables and given/known data

    Hi.
    The equation is: yt= c1 Lambda1t+c2 Lambda2t

    where c1 and c2 are constants.
    In general, is this equation divergent or convergent?

    If divergent, what condition is required to make it convergent?


    3. The attempt at a solution
    I know that letting t be a negative number, I can make it convergent. But I know that there is more to that answer.

    Please help! Thanks.
     
  2. jcsd
  3. Jan 14, 2012 #2

    Mark44

    Staff: Mentor

    This is a little cleaner...
    [tex]y_t = c_1 \lambda_1^t + c_2 \lambda_2^t[/tex]

    You can rewrite at as (eln (a))t = et*ln(a), provided that a > 0.

    For your equation you need to look at possible restrictions on the two lambdas.
     
  4. Jan 14, 2012 #3
    OK, I found out that the function

    c1et(lnθ1 ) +c2et(lnθ_2 ) is convergent only when 0<θ1, θ2<1.

    All done.
    Thanks.
     
    Last edited: Jan 14, 2012
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