Determine a formula where $f: \mathbb{N}\rightarrow \mathbb{N} $ and $f$ is given by $ f(n+2)=(1/2)(f(n+1)+f(n))$.
Show that the sequence $a_1=1$, $a_2=2$, $a_{n+2} = (a_{n+1}+a_n)/2$ converges by showing it is Cauchy