Let $$a_{1}, a _{2}......$$ be a Fibonacci series.
I have a book which has a problem under the "mathematical induction" chapter, which asks me to prove
$$a _{n+1}^{2}=a _{n}a _{n+2}=(-1)^{n}$$

I think the statement is incorrect. For n=1, we don't have the statement correct, and I can't expect it to be correct for n1 as $$(-1)^{n}$$ will always only have values either +1 or -1, and the expression $$a _{n}a _{n+2}$$ will have increasing value.

Do you think I am correct, or is there really a prove for the statement.
Please provide me some help.

Question

Let $$a_{1}, a _{2}......$$ be a Fibonacci series.
I have a book which has a problem under the "mathematical induction" chapter, which asks me to prove 
$$a _{n+1}^{2}=a _{n}a _{n+2}=(-1)^{n}$$

I think the statement is incorrect. For n=1, we don't have the statement correct, and I can't expect it to be correct for n>1 as $$(-1)^{n}$$ will always only have values either +1 or -1, and the expression $$a _{n}a _{n+2}$$ will have increasing value.

Do you think I am correct, or is there really a prove for the statement. 
Please provide me some help.

anonymous · Answer

$$a_{n+2}a_n-a_{n+1}^2=(-)^n$$is a true statement.

anonymous · Answer

But the statement given there is not correct, am I right?

anonymous · Answer

So your '=' sign is not a typo.?

anonymous · Answer

No

anonymous · Answer

When then it's incorrect.

anonymous · Answer

It should be a minus sign.

anonymous · Answer

Thanks  A LOT

anonymous · Answer

np

anonymous · Answer

I told you a genius like you will need a look to solve the problem

anonymous · Answer

You don't have any idea, what help you are providing just free of cost

anonymous · Answer

Anyways, You are a busy person, so I must not hold you here,
Bye

anonymous · Answer

:)  I haven't had a chance to look at the other question yet.  I'm thinking the problem can be solved by proving first that linking the last contestant to fight the one left over at the beginning is the same as linking the new (k+1) guy to somewhere else in the system.  Once that's done, the induction is as we said.

anonymous · Answer

That sounds awkward.

anonymous · Answer

I should have more time in the middle of the week.  When is STEP?

anonymous · Answer

20th June 2011 PM	STEP Paper II takes place 
22nd June 2011 PM	STEP Paper III takes place 
24th June 2011 AM	STEP Paper I takes place

anonymous · Answer

ok...plenty of time!

anonymous · Answer

Yes thats true

anonymous · Answer

Alright, I have to go do some work.  Like I said, middle of the week will be better.

anonymous · Answer

But I am taking several other similar exams, which you haven't heard of

anonymous · Answer

Sure bye now

anonymous · Answer

What are you intending to do with the results of the exams?

anonymous · Answer

I will email that to you. People will not like me saying such things here. They will think i am too presumptuous

anonymous · Answer

ok

anonymous · Answer

i'm off now.  happy studies.

anonymous · Answer

Thanks and bye