Formula using fibonacci numbers Let $a_n$ be the $n^{th}$ term of the sequence defined recursively by
 $a_{n+1} = \frac {1}{1+a_n}$
and let $a_1 = 1.$ Find a formula for $a_n$ in terms of the Fibonacci numbers $F_n$. Prove that the formula you found is valid for all natural numbers $n.$ 
Wow can I solve this type of problem?
And, how to prove it by induction? Do i solve for $a_n$ or what? I'm new to this chaper( sequences and series).

By induction $a_n=\frac{F_n}{F_{n+1}}$ because $a_1=\frac{F_1}{F_2}=1$ and
$$a_{n+1}=\frac{1}{1+a_n}=\frac{1}{1+\frac{F_n}{F_{n+1}}}=\frac{F_{n+1}}{F_{n+2}}.$$
$\{F_n\}:1,1,2,3,5,...$.
