This is a "study guide" question for a test I am trying to figure out. The sequence given is
$a_k=\dfrac{2}{a_{k-1}}$ for all integers $k\ge2$, and $a_1=1$.
It then asks me to find an explicit formula and prove it with "strong" induction. I came up with the following explicit formula:
$a_k=\dfrac{(-1)^k+3}{2}$
But I have no idea how to implement the proof of this. I understand that strong induction is like a normal mathematical induction proof but instead of proving for $k+1$ I need to prove for a range? I'm just not sure what my inductive hypothesis and base cases are for this problem. Thanks for any help!