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Fibonacci Sequences

Let (f_k) be the Fibonacci sequence, show that:

a) For every integer n>= 0, we have f_4(n+1) = 3f_4n+1 + 2f_4n

b) Use a) in order to prove by induction that ∀n Є N, 3 | f_4n

Solution Preview

Hi, here is the solution...

Let (f_k) be the fibonacci sequece.

the Fibonacci numbers form a sequence defined by

f_k = { 0, if k=0
1, if k=1
f_(k-1)+f_(k-2) if k>1

f_k= 0,1,1,2,3,5,8,13,21.........

Here, f_0 =0, f_1=1, f_2=1

a) For every integer ...

Solution Summary

A Fibonacci sequence is investigated.