Proving Cassini's identity
Maths and statistics discussion, revision, exam and homework help.
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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. -
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Re: Proving Cassini's identityI have no clue what this identity is, but are you sureyou'renotmissing a definition of
such that
?
DoesSince 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. -
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Re: Proving Cassini's identityYes 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.(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.
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. -
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Re: Proving Cassini's identityThink I get it now, yet another newb error from me, not seeing the obvious(Original post by aznkid66)
I have no clue what this identity is, but are you sureyou'renotmissing a definition of such that
?
DoesSince 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.
Substitution of 
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Re: Proving Cassini's identityLol, my inner newb gets abused too much for my liking at times.(Original post by aznkid66)
Evil textbooks are always trying to take advantage of our inner newb, lol xD
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. -
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Re: Proving Cassini's identityIt's subbing(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?
into what's in the parentheses. low equals high minus middle.
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Re: Proving Cassini's identityHow do we know(Original post by aznkid66)
It's subbing into what's in the parentheses. low equals high minus middle?.
?
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. -
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Re: Proving Cassini's identityI 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.(Original post by SubAtomic)
How do we know ?
Any online material I can read to understand this better?
As for that specific equation, there are many places you can start. For example, your book defines the recursive equation as:
Route 1:
Spoiler:ShowRight 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:ShowRight 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. -
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Re: Proving Cassini's identityYou're a star, thanks for that, cannot rep you again yet but that really explains it well(Original post by aznkid66)
I don't know, I haven't formally learned this before, so I don't know any sources..
it is so good I could 
lol
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(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.
Last edited by SubAtomic; 04-07-2012 at 20:26.
Substitution of 
