The question I'm trying to do is this:
Assume $x>2$ and $n=\lfloor x/2\rfloor$. Show that $\psi(x)>(x-2)\log2-\log(x+1)$, given the inequality $2n\log2-\log(2n+1)<\psi(2n)$.
All I've really done is substitute $n$ in to get
$2\lfloor x/2\rfloor\log2-\log(2\lfloor x/2\rfloor+1)<\psi(2\lfloor x/2\rfloor)$
No idea what to do.. could it be a manipulation involving $\lfloor 2x\rfloor- 2\lfloor x\rfloor=0$ or $1$?