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.

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