MathNet 2022-part-04 — 197 problems (EN–VI) Question 146

Consider the positive numbers $x_1, x_2, \dots, x_n$ such that $\sum_{i=1}^n x_i = \sum_{i=1}^n \frac{1}{x_i}$. Prove that $\sum_{i=1}^n \frac{1}{n-1+x_i} \le 1$.