Question 6
(CAN 3) Let $c$ be a positive integer. The sequence $\{f_n\}$ is defined as follows:
$$f_1=1,\quad f_2=c,\quad f_{n+1}=2f_n-f_{n-1}+2\qquad(n\ge2).$$
Show that for each $k\in\mathbb N$ there exists $r\in\mathbb N$ such that $f_kf_{k+1}=f_r$.
$$f_1=1,\quad f_2=c,\quad f_{n+1}=2f_n-f_{n-1}+2\qquad(n\ge2).$$
Show that for each $k\in\mathbb N$ there exists $r\in\mathbb N$ such that $f_kf_{k+1}=f_r$.