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Q10 Write a recursive function to obtain the first 25 numbers of a Fibonacci sequence. In a Fibonacci sequence the sum of two successive terms gives the third term. Following are the first few terms of the Fibonacci sequence: 1 1 2 3 5 8 12 21 34 55 89 - EASTER SCIENCE
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SOLVED: The Fibonacci numbers f0, f1, f2, . . . are a sequence of numbers that are defined as follows: we set f0 := 0 and f1 := 1, and for k ∈ N with k ≥ 2 we have fk := fk−1 fk−2.• Prove the following matrix identity: for all n ∈ N we have(fn 1 fn) (1 1)^n —- 2 by 2 matrix(fn fn−1) (1 0) —> matrix• Prove the following identity: for all n ∈ N we have (−1)^n = (fn 1)(fn−1) − (fn)^2.• Prove that for all n ∈ N0 we have (f2n 1) = (fn)^2
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