Fibonacci

Discrete Mathematics Level pending

Given: $\begin{cases} f_{n} = f_{n-1}+f_{n-2}, & n\geq2 \\ f_{0}=0 \\ f_{1}=1 \end{cases}$

$$f_{n}$$ can be expressed in the following form:

$f_{n} = \frac {1}{a} \left ( \frac{1+a}{b} \right )^{n} - \frac {1}{a} \left ( \frac {1-a}{b} \right )^{n} \text{ for }n\geq0$

Find $$a+b$$ to three decimal places.

×