Interesting question on Fibonacci numbers.

Question

Ran across this interesting question about the Fibonacci numbers but quite unsure how to go about it, any ideas ?

For instance, the idea that comes after the word "Hint:" – Mar 29 '16 at 20:23 — , Mar 29 '16 at 20:23

score 2 · Answer 1 · answered Mar 29 '16 at 20:29

hint for second part$$f_{n+1}=f_n+f_{n-1}\\f_{n}=f_n+0\\\to\\$$ $$f_{n+1}=f_n+f_{n-1}\\f_{n}=f_n+0f_{n-1}$$ $$\left(\begin{array}{c}f_{n+1}\\ f_{n}\end{array}\right)=\begin{bmatrix}a & b \\c & d \end{bmatrix}.\left(\begin{array}{c}f_{n}\\ f_{n-1}\end{array}\right)\\\left(\begin{array}{c}f_{n+1}\\ f_{n}\end{array}\right)=\begin{bmatrix}1 & 1 \\1 & 0 \end{bmatrix}.\left(\begin{array}{c}f_{n}\\ f_{n-1}\end{array}\right)$$

Interesting question on Fibonacci numbers.

1 Answers1