Prove the following properties of the Fibonacci sequence using the proof method spec- ified: (a)Fn = 5Fn−4 + 3Fn−5, for n ≥ 6 using a direct proof. (b) F1 + F2 + F3 + · · · + Fn = Fn+2 − 1 using a proof by induction

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Problems on Growing Functions

For a given set of functions f and g, the growth of functions states that the function g grows as fast as the function f. The growth rate of algorithms helps determine the algorithm's efficiency and compare its performance to other algorithms.