Question 111
Prove that for all positive real numbers $a, b$ and every positive integer $n$, the inequality
$$
(a+b)^n - a^n - b^n \ge \frac{2^n-2}{2^{n-2}} \cdot ab(a+b)^{n-2}
$$
holds.
$$
(a+b)^n - a^n - b^n \ge \frac{2^n-2}{2^{n-2}} \cdot ab(a+b)^{n-2}
$$
holds.