Use induction to prove that the following identity holds for any fixed k: FkFn + Fk+1Fn+1...

Question

Question

Use induction to prove that the following identity holds for any fixed k:

FkFn + Fk+1Fn+1 = Fn+k+1

Recall the definition of the fibonacci numbers: F0 = 0, F1 = 1, and Fn = Fn−1 + Fn−2.

engineering Computer-Science

Answer 1

Answer #1

Using induction

base case for n=0

Hence the statement is true for n=0

Inductive hypotheses:-assuming the statement is true for n<=m

Step: for n=m+1

(using inductive hypothesis for n=m and n=m-1)

Hence proved

Answer 2

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