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1. Linear second-order recurrence sequence
#Edit: Changed to undergrad because it seems not many if any have seen this in sixth form.

Hi, having a brain malfunction with this as am not quite understanding. Maybe am brain fluffing on some basic indices? Not quite understanding the RHS.

To find a closed form for a linear second-order recurrence system:

Step 1 Write down the auxiliary equation:

Step 2 Solve the auxiliary equation:

Step 3 Write down the general solution with unkown constants A and B.

Step 4 Use initial terms to find A and B.

Why does

Auxiliary equation:

Recurrence relation:

am I right in my implies here?

Maybe getting it a bit more now after typing it out but still unsure.

So with a bracket like this

No I'd have

Check:

think I get it now, maybe maybe not .

Missed how the last term of the second line takes the first term coefficient down to 1

Still feel a bit puzzled.
Last edited by SubAtomic; 04-07-2012 at 18:29.
2. Re: Linear second-order recurrence sequence

(Original post by nuodai)
...

(Original post by notnek)
...
neg: Really? Tool
Last edited by SubAtomic; 09-07-2012 at 19:07.
3. Re: Linear second-order recurrence sequence
(Original post by SubAtomic)
Any takers?
Which equation is
4. Re: Linear second-order recurrence sequence
(Original post by SubAtomic)
The only equation on the page with the * next to it is this and it is layed out like this

And then a little box with a few things in like this

I haven't covered this topic, so sorry i can't help.

5. Re: Linear second-order recurrence sequence
(Original post by raheem94)
I haven't covered this topic, so sorry i can't help.

Ok cheers for looking mate.

6. Re: Linear second-order recurrence sequence
(Original post by BabyMaths)
If is a root of whether it's repeated or not it follows that and an extra factor of n isn't going to change that. and so and so satisfies .

There is a more interesting question to ask here.

Was going to completely change my post and break it into what I don't quite get.

So will go from the first things just to clarify.

I think I was multiplying this out wrong to start off. Everything above is copied from a book so I tried working through it and that is where I became confused.

Realised after messing about last night that I was expanding the bracket wrong.

So I thought this

Which is wrong, yes, or am I making a newb error?

So I'd have been better bringing the to the right hand side to start with?

And is this line mathematically correct

Last edited by SubAtomic; 21-06-2012 at 12:44.
7. Re: Linear second-order recurrence sequence
Also please don't use * for anything other than conjugate.
8. Re: Linear second-order recurrence sequence
(Original post by FranticMind)
Also please don't use * for anything other than conjugate.
what do you mean?
9. Re: Linear second-order recurrence sequence
(Original post by SubAtomic)
So I'd have been better bringing the to the right hand side to start with?

And is this line mathematically correct

Yes to everything here.
10. Re: Linear second-order recurrence sequence
(Original post by BabyMaths)
Yes to everything here.
Thanks, that is where most of my confusion came from.

So what is the more interesting question to ask
11. Re: Linear second-order recurrence sequence
(Original post by SubAtomic)
So is this correct too then?

I'm not sure what you're trying to do.

The more interesting question I had in mind was why the solution in the case of repeated roots is .
12. Re: Linear second-order recurrence sequence
(Original post by BabyMaths)
I'm not sure what you're trying to do.
Just trying to understand what I was thinking the other day, because I was way off the mark it seems.

(Original post by BabyMaths)
Do you mean

(Original post by BabyMaths)
The more interesting question I had in mind was why the solution in the case of repeated roots is .
No idea That is a question for you to answer Will have to dwell on this or maybe I will have a better idea once I have finished the block I am currently on.

Thanks a lot for clarifying those things though

All the best.
Last edited by SubAtomic; 21-06-2012 at 13:54.
13. Re: Linear second-order recurrence sequence
Sorry, my post that you +repped was rubbish.

I will try to redeem myself.

With the proposed solution

We have

Subbing these in we get .

Collecting terms and factorising a bit..

and we know that since we have equal roots and also so satisfies .

Edit: I missed a B.
Last edited by BabyMaths; 21-06-2012 at 21:10.
14. Re: Linear second-order recurrence sequence
(Original post by SubAtomic)
what do you mean?
I think he meant stuff like complex conjugate. Example is a conjugate of
15. Re: Linear second-order recurrence sequence
(Original post by BabyMaths)
Sorry, my post that you +repped was rubbish.

I will try to redeem myself.

With the proposed solution

We have

Subbing these in we get .

Collecting terms and factorising a bit..

and we know that since we have equal roots and also so satisfies .
Wonderful, + repped you for your time but this has made things much clearer, your explanation is better than the book, thanks

(Original post by raheem94)
I think he meant stuff like complex conjugate. Example is a conjugate of
Well he wasted his time telling me that because I don't have complex numbers until the final block

Thought it'd be clear what it meant.
Last edited by SubAtomic; 28-06-2012 at 17:54.
16. Re: Linear second-order recurrence sequence
Hi, not quite sure what my book is saying here.

I have a table, Coefficients p and q, Initial values a and b, and

Apparent pattern in

Both coefficients have value 1, Initial values a=0 and b=1.

So this is what the book says under the 'apparent pattern' section,

it is every other term of , starting with

Will post some screen shots of what mathcad shows. I don't get it, what does it mean it is every other term of , starting with .

The first screen shot is of p=1, q=1, a=0, b=1.
Attached Thumbnails

17. Re: Linear second-order recurrence sequence
could you post a book/page ref if it's MS221?
18. Re: Linear second-order recurrence sequence
(Original post by sputum)
could you post a book/page ref if it's MS221?
Lol, I bought the materials for 221 online to go through before October.

Not sure if the course books are the same throughout the years but the page number is 10 in computer book A, table 4.2.

Don't get what it is saying in the top line
19. Re: Linear second-order recurrence sequence
(Original post by SubAtomic)
Hi, not quite sure what my book is saying here.

I have a table, Coefficients p and q, Initial values a and b, and

Apparent pattern in

Both coefficients have value 1, Initial values a=0 and b=1.

So this is what the book says under the 'apparent pattern' section,

it is every other term of , starting with

Will post some screen shots of what mathcad shows. I don't get it, what does it mean it is every other term of , starting with .
What are U_3, U_5, U_7, U_9, ...? Compare with the values for .
20. Re: Linear second-order recurrence sequence
(Original post by DFranklin)
What are U_3, U_5, U_7, U_9, ...? Compare with the values for .
Can see that

Just not too sure on the wording every other term