Prove that the number

(

is rational if and only if n is even.

(I think going one way if n is even then its clear that its rational, what about assuming that n is even then the number is rational? Is it inductive?)

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- Jan 13th 2009, 09:07 AMJason BourneRational number if n is even proof
Prove that the number

(

is rational if and only if n is even.

(I think going one way if n is even then its clear that its rational, what about assuming that n is even then the number is rational? Is it inductive?) - Jan 13th 2009, 09:37 AMrunning-gag
Hi

You can use Newton's formula to develop and then study the 2 cases (n even and n odd).

When n is even all the terms involving disappear. - Jan 13th 2009, 10:17 AMJason Bourne
Newton's formula?

- Jan 13th 2009, 10:42 AMrunning-gag
Sorry I don't know how it is called in English

I am talking about this formula

- Jan 15th 2009, 11:19 AMThePerfectHacker
Consider the sequence defined as:

Certaintly, the terms of the sequence are integers.

Furthermore, the solution to this recurrence relation is given by: .

If is__even__then

Consider the Fibonacci sequence it satifies

Define .

If is__odd__then .

Therefore for odd we have .