Question 117
Prove for integers $n$ that
$$
\left\lfloor\frac{n}{2}\right\rfloor\left\lfloor\frac{n+1}{2}\right\rfloor=\left\lfloor\frac{n^{2}}{4}\right\rfloor .
$$
$$
\left\lfloor\frac{n}{2}\right\rfloor\left\lfloor\frac{n+1}{2}\right\rfloor=\left\lfloor\frac{n^{2}}{4}\right\rfloor .
$$