In my previous post on Fibonacci-style sequences, I gave the formulae for the closed form

given the recurrence values where

but I did not show that the formula is valid. I do that here.

In that previous post, the closed form was derived from its applications to .

We need to demonstrate that the formula continues to be valid for other values of *n*.

There, we showed that

We proceed by induction.

Consider two cases to be valid (as inductive hypotheses):

Now

We have at least two base cases available. Hence by induction, the formula holds for all *n*.

### Like this:

Like Loading...

*Related*

This entry was posted on Tuesday, 1 October 2013 at 19:26 and is filed under Contribution, Mathematics. You can follow any responses to this entry through the RSS 2.0 feed.
You can leave a response, or trackback from your own site.

## Leave a Reply