Question 10
(AUS) Let $r_1,r_2,\ldots,r_n$ be real numbers greater than or equal to $1$. Prove that
$$\frac1{r_1+1}+\frac1{r_2+1}+\cdots+\frac1{r_n+1}\ge\frac{n}{\sqrt[n]{r_1r_2\cdots r_n}+1}.$$
$$\frac1{r_1+1}+\frac1{r_2+1}+\cdots+\frac1{r_n+1}\ge\frac{n}{\sqrt[n]{r_1r_2\cdots r_n}+1}.$$