Prove for any $x \geq 1$ that

$$\left( \sum_{n=0}^{\infty} (n+x)^{-2} \right)^2 \geq 2 \sum_{n=0}^{\infty} (n+x)^{-3}.$$

The best solution was submitted by 김기수 (KAIST 수리과학과 18학번, +4). Congratulations!

Here is the best solution of problem 2022-13.

Another solution was submitted by 김찬우 (연세대학교 수학과, +3).