Hee, I got a really simple recurrence relation:

with .

Calculating a few values we easily notice ,

but how is this formally derived?

Can someone offer a quick insight?

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- Oct 15th 2011, 10:02 AMDinkydoeRecurrence relation
Hee, I got a really simple recurrence relation:

with .

Calculating a few values we easily notice ,

but how is this formally derived?

Can someone offer a quick insight? - Oct 15th 2011, 11:19 AMMooRe: Recurrence relation
Hello,

I guess you're a little wrong with your few values, for example, I get - Oct 15th 2011, 11:39 AMDinkydoeRe: Recurrence relation
Yes, that's quite annoying...

It shouldve been - Oct 15th 2011, 12:30 PMemakarovRe: Recurrence relation
- Oct 15th 2011, 11:27 PMchisigmaRe: Recurrence relation
The difference equation...

(1)

... is non-linear and in most cases like that an*ad hoc*solving procedure has to be found. In this particular case it is easy to see that the solution is a continued fraction...

(2)

... where . Now if You use the standard algorithm to write the rational number in term of continued fraction You obtain exactly the expression (2) so that is...

(3)

Kind regards