# Fibonacci generating functions for pair/impair indexes.

• March 19th 2013, 03:18 PM
vercammen
Fibonacci generating functions for pair/impair indexes.
Let $f_n$ be the sequence of Fibonacci numbers.
It's known that $\sum_{n \ge 0} f_n x^n = \dfrac{1}{1-x-x^2}$
What is the interpretation of this for $\sum_{n \ge 0} f_{2n} x^n \text{ and }\sum_{n \ge 0} f_{2n+1} x^n\text{ ?}$
How do we prove it?