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# Proving Cassini's identity Tweet

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1. Proving Cassini's identity

Know from a previous page that, Fib recurrence relation is

Hi, so here's Cassini' identity

Cassini's identity

So what's the deal with subscripts because this is where I get lost.

Using the Fib recurrence relation twice.

We have

How do we go from the first line to the second line, I think this is what is holding me back.

So I can gather from the equation that

Just don't understand how the factorising works here

Will put the rest up but that bit is the main bit for me so far, maybe will get the rest if I knew what going on within those first lines.

Last edited by SubAtomic; 04-07-2012 at 19:28.
2. Re: Proving Cassini's identity
I have no clue what this identity is, but are you sure you're not missing a definition of such that

?

Does Since F stand for the fibonacci sequence? If so, what's happening is a substitution for using the recursive formula of the sequence.

Do you have any more questions after that point? If you do, what they only do in the next step is a mixture of expanding and factorizing.
Last edited by aznkid66; 04-07-2012 at 19:19. Reason: Just read up on it.
3. Re: Proving Cassini's identity
(Original post by aznkid66)
I have no clue what this identity is, but are you sure you're not missing a definition of such that

?

Does F stand for the fibonacci sequence? If so, what's happening is a substitution for using the recursive formula of the sequence.
Yes it is to do with Fibs, and yes the 'good idea' is using the Fib recurrence relation twice assuming that is what you mean by recursive.

It's to do with telescoping cancellation I think.

Already know the Fib sequence is specified by recurrence system

from an earlier chapter if that is supposed to help my understanding?

Other than that everything I have in front of me is in the OP.

Ah, this is on the page before which may explain things better.

Which is a rearrangement of the Fibonacci recurrence relation.
Last edited by SubAtomic; 04-07-2012 at 19:22.
4. Re: Proving Cassini's identity
Yes, that's the substitution made in:

(Original post by SubAtomic)

I thought you were having trouble somewhere before that, sorry.
5. Re: Proving Cassini's identity
(Original post by aznkid66)
I have no clue what this identity is, but are you sure you're not missing a definition of such that

?

Does Since F stand for the fibonacci sequence? If so, what's happening is a substitution for using the recursive formula of the sequence.

Do you have any more questions after that point? If you do, what they only do in the next step is a mixture of expanding and factorizing.
Think I get it now, yet another newb error from me, not seeing the obvious Substitution of
6. Re: Proving Cassini's identity
Evil textbooks are always trying to take advantage of our inner newb, lol xD
7. Re: Proving Cassini's identity
(Original post by aznkid66)
Evil textbooks are always trying to take advantage of our inner newb, lol xD
Lol, my inner newb gets abused too much for my liking at times.

Just for clarification how would I multiply out such an equation

Don't get how

Or is it all to do with subbing in stuff we already should know?

Gosh I suck at this stuff so far.
Last edited by SubAtomic; 04-07-2012 at 19:57.
8. Re: Proving Cassini's identity
(Original post by SubAtomic)
Lol, my inner newb gets abused too much for my liking at times.

Just for clarification how would I multiply out such an equation

Or is it all to do with subbing in stuff we already should know?
It's subbing into what's in the parentheses. low equals high minus middle.
9. Re: Proving Cassini's identity
(Original post by aznkid66)
It's subbing into what's in the parentheses. low equals high minus middle?.
How do we know ?

Any online material I can read to understand this better? Feel I must be missing something.
Last edited by SubAtomic; 04-07-2012 at 20:06.
10. Re: Proving Cassini's identity
(Original post by SubAtomic)
How do we know ?

Any online material I can read to understand this better?
I don't know, I haven't formally learned this before, so I don't know any sources.. I think most of it can be "logic'd" with algebra as long as you have a grasp on sequences and using the subscripts to your advantage.

As for that specific equation, there are many places you can start. For example, your book defines the recursive equation as:

Route 1:
Spoiler:
Show
Right now, that equation says "high = middle + low." So we isolate "low" by moving "middle" to the LHS.

Move everything down the sequence to change into .

Route 2:
Spoiler:
Show
Right now, that equation says "high = middle + low." Currently, the "low" is , so move everything down a sequence to change the "low" into .

Now isolate the term you want, , by moving to the LHS.

Last edited by aznkid66; 04-07-2012 at 20:13. Reason: Added stuff to the beginning.
11. Re: Proving Cassini's identity
(Original post by aznkid66)
I don't know, I haven't formally learned this before, so I don't know any sources..
You're a star, thanks for that, cannot rep you again yet but that really explains it well it is so good I could lol

(Original post by aznkid66)
I think most of it can be "logic'd" with algebra as long as you have a grasp on sequences and using the subscripts to your advantage.
Well with your explanation I hope to be able to use subscripts to my advantage in the future if such a problem occurs, many thanks
Last edited by SubAtomic; 04-07-2012 at 20:26.