Complex Analysis - Partial Fraction Decomposition

Hey guys. This might not be quite the right place on the forum, but here goes. I have this assignment that I have almost completed, but I can't quite figure out the last bit. Could anyone give me a helping hand?

Prove that , and (This is the sequence of fibonacci numbers: 0, 1, 1, 2, 3, 5, 8,...).

Find the partial fraction decomposition of the rational function and use it to prove Binet's formula:

(1)

Alright, I have shown that and are simple poles of and I've found out that the partial fraction decomposition of is:

(2)

I just have no idea how to use that, to show (2) from (1). Can someone give me a clue?

/Morten

Re: Complex Analysis - Partial Fraction Decomposition

Find the partial fractions decomposition of **what** rational function? I don't see anywhere that you say what rational function you are talking about.

Re: Complex Analysis - Partial Fraction Decomposition

Arh sorry.. Apparently it only pasted half of the assignment into the post. Here is the first half of the assignment:

Prove that the function has simple poles at and determine the radius of convergence of the power series:

So the rational function is

Re: Complex Analysis - Partial Fraction Decomposition

Surely you understand that the poles are where the denominator is 0...