# How to determine convergence/divergence?

1. Jan 14, 2012

### Kinetica

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.

2. Jan 14, 2012

### Staff: Mentor

This is a little cleaner...
$$y_t = c_1 \lambda_1^t + c_2 \lambda_2^t$$

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.

3. Jan 14, 2012

### Kinetica

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