Fibonacci Corrected

You all getting wrong the first terms of the series. The correct one is:

0, 1, 1, 2, 3, 5, 8, 13 ...

Hence, F(0)=0, F(1)=1
and F(n)=F(n-1)+F(n-2)


Joe Back

Prove F(-N) = -F(N) when N is even.

Difficult really, since that is simply the definition of an even function. It's like saying prove dy/dx = lim delta(y)/delta(x) as delta tends towards 0. It's just the definition.

!LKH's formula can be written as:

F(-n) = -(-1)ⁿF(n)

Proof: For Fib series we know,

F(n) = F(n-1) + F(n-2)

So, F(n-2) = F(n) - F(n-1).

Therefore, Fib series, when extended to negative numbers become:

Code:

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... -8, 5, -3, 2, -1, 1, 0, 1, 1, 2, 3, 5, 8, ...

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When n is -1, answer is 1 (for n=1, ans=1), and when n = -2, answer is -1 (for n=2, ans=1) and so on.

Quote:

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Originally Posted by Mattywoo2

Difficult really, since that is simply the definition of an even function. It's like saying prove dy/dx = lim delta(y)/delta(x) as delta tends towards 0. It's just the definition.

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You're misunderstanding the question - the question stated you should prove the result when N is even, not when the function is even.