c1≈2.5]]>

I really didn't get what you were trying to do with that recursive equation or else I'd help

Solve it?

It's a second order linear homogemous recurrent relation with constant coefficients.

I already found a general solution to them (the CE), but it's missing two constants, which can be filled in. The bottom half is me attempting to do that, and failing.

]]>Characteristic equation:

Check:

Okay, I'm doing something wrong here.

Simple way won't work, using ABC formula:

So the worked out CE is:

Anyone care to calculate c1 and c2?

Is it getting ugly yet?

Using the approximations:

Help?

]]>