Fibonacci Sequences
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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
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Solution Summary
A Fibonacci sequence is investigated. The integer function are solved in order to prove by inductions.
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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 ...
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