Help with linear homogeneous recurrence relations

[Bucs44]

Homework Statement

Here's my problem - Give the order of linear homogeneous recurrence relations with constant coefficients for: An = 2na(n-1)

The Attempt at a Solution

I have no idea on how to start this problem - Any help would be greatly appreciated.

 

[HallsofIvy]

First, I think you mean A_n= 2A_n-1. Be careful to distinguish between "A" and "a"!

Notice that this problem does not (yet) ask you to solve the equation! It just asks that you state its order. Do you know the definition of "order" of a recurrence relation? I suspect the way to "start this problem" is to look up "order"!

 

[Bucs44]

=2(2An-1 + 1) + 1
=2^2An-1 + 2 + 1

Is this right?

 

[Bucs44]

The order is just the number of "previous" terms, in which case the order is 2

 

[HallsofIvy]

No, in the recursion A_n= 2A_n-1, A_n depends on the value of A one place before it. The order is 1.

As for

=2(2An-1 + 1) + 1
=2^2An-1 + 2 + 1

I can't tell whether it is correct or not because you haven't told me what it is supposed to equal!

Once again, is this intended to be A_n= 2S_n-1? If so, I cannot see where you are getting the "+1" terms from.

Suppose A₀= 1. What is A₁? A₂?