Consider the expression
$$\left\lfloor\frac{2n-1}{2}\right\rfloor\;:$$
does it make sense that this floor function will evaluate to $n$? Or should it be $n-1$?
Consider the expression
$$\left\lfloor\frac{2n-1}{2}\right\rfloor\;:$$
does it make sense that this floor function will evaluate to $n$? Or should it be $n-1$?
$\frac{2n-1}{2}=n-\frac{1}{2}$, so the floor is $n-1$.