Let $ P(n)$ be the lowest number of steps necessary to make n cards turned down. Now we will find the relation between $ P(n)$ and $ P(n+1)$. $P(n+1)$ is equivalent to the number of smallest steps necessary to make $n+1$ cards turned down, first we will choose the top n cards as we know we can make them turn down in $P(n)$ steps, also there is one card left on the bottom and we will flip the whole set of $n+1$ cards if all of them are looking up. So, $P(n+1)=P(n)+1 \implies P(n)=n$ considering $P(1)=1$, so $P(n)=n$ and we are done.