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?