Question 155
Let $m$ and $n$ be nonzero natural numbers. Prove that
$$
\frac{(m+n)!}{(m+n)^{m+n}} \lt \frac{m!}{m^{m}} \frac{n!}{n^{n}}
$$
$$
\frac{(m+n)!}{(m+n)^{m+n}} \lt \frac{m!}{m^{m}} \frac{n!}{n^{n}}
$$
MathNet 2017-part-02 — 176 problems (EN–VI) Question 155
Math Olympiad Vault · MathNet 2017-part-02 — 176 problems (EN–VI)