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#1 Re: Help Me ! » Fibonacci sequence » 2008-07-14 12:00:12
It appeared to be more involved than that when reading it in my textbook... I didnt know it was simply just adding a term to both sides of the equation that represents the next term. Thats the overall gist of it right?
So what you showed up above is actually proving that n=k+1; meaning the recurrence is proved. Is that all there is to it?
Man they make these things seem more complicated than they have to be.
Thanks alot for your help JaneFairfax... this will help alot in the coming weeks.
#2 Re: Help Me ! » Fibonacci sequence » 2008-07-14 11:29:11
The n=1 part I understand, no problems there... I understand the assumption that n=k form... I don't understand why you added F(2(k+1)) to both sides... I get that it has something to do with proving the recurrence relationship (proving that n=k+1 is true). Could you elaborate on that a little?
#3 Re: Help Me ! » Fibonacci sequence » 2008-07-14 10:38:46
Start by trying to write F(2k+2) in terms of F(2k)
Like this?
Then I guess F(2(k+1)+1) would be
Am I going in the right direction or did I not get what you were asking?
Check your formula. I dont think its the correct formula for the Fibonacci sequence.
The full problem directly from the worksheet is
. I hope that helps... I figured the beginning part was not important in this part of it.#4 Help Me ! » Fibonacci sequence » 2008-07-14 06:17:46
- javadude
- Replies: 7
Ok, another part that Im confused on... I cant seem to wrap my head around this proving by induction. We are asked to prove a particular fibonacci sequence. I have the base step and the I got the inductive hypothesis I think... but I cannot figure out how to do the actual proof.
The fibonacci sequence is
My inductive hypothesis is
I've tried so many different ways but I cannot figure out how to prove this... Can someone help me by pushing me into the right direction? Thanks!
#5 Re: Help Me ! » Discrete Math - Proofs by Set Identities » 2008-07-13 11:05:41
wow... I can't believe how stupid I feel now... its so obvious. I suppose it always is though once you see it done.
Thanks alot JaneFairfax, now onto combinatorics 
#6 Help Me ! » Discrete Math - Proofs by Set Identities » 2008-07-13 09:13:20
- javadude
- Replies: 2
Hey everyone, Im taking a course in Discrete math and am having a hard time with some of these topics. For instance, Im given
(A ∪ C) ∩ [ (A ∩ B) ∪ (C' ∩ B) ] = A ∩ B
Im asked to prove this by set identities. Ive made the first step using the distributive property to achieve
(A ∪ C) ∩ (A ∩ B) ∪ (A ∪ C) ∩ (C' ∩ B)
Now, I can see im obviously suppose to somehow get C and C' together so they cancel out to a null set. Im lost as to what direction to take? Can someone lend a helping hand?
Thanks alot in advance!
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